Bigdelim help

Ma trận đặc biệt và gói lệnh
bigdelim.sty
Nguyễn Hữu Điển
Khoa Toán - Cơ - Tin học
ĐHKHTN Hà Nội, ĐHQGHN
1 Loại ma trận góc dưới tam giác
begin{equation*}
{mathbf B} = { b_{ij} }_{i,j=1,dots,n} = left(%
begin{array}{cccccc}
ast & ast & ast & ldots & ast & ast
ast & ast & ast & ldots & ast & ast
& ast & ast & ldots & ast & ast
& &ddots& ddots & vdots & vdots
& text{huge{0}} & &ddots & ast & ast
& & & & ast & ast
end{array}%
right)
end{equation*}
B = {bij}i,j=1,...,n =










∗ ∗ ∗ . . . ∗ ∗
∗ ∗ ∗ . . . ∗ ∗
∗ ∗ . . . ∗ ∗
...
...
...
...
0 ... ∗ ∗
∗ ∗










begin{equation*}
{mathbf B}= left(%
begin{array}{ccccccccccc}
ast && ast && ast && ldots && ast && ast
&ddots & && && && &&
ast && ast && ast && ldots && ast && ast
&ddots& &ddots&&& && &&
&& ast && ast && ldots && ast && ast
1

http://nhdien.wordpress.com - Nguyễn Hữu Điển 2
&& &ddots& &ddots& && &&
&& && && && vdots && vdots
&& && &ddots& &ddots& &&
&& text{huge{0}} && &&ddots && ast && ast
&& && && &ddots& &ddots&
&& && && && ast && ast
end{array}%
right)
end{equation*}
B =

























∗ ∗ ∗ . . . ∗ ∗
...
∗ ∗ ∗ . . . ∗ ∗
...
...
∗ ∗ . . . ∗ ∗
...
...
...
...
...
...
0 ... ∗ ∗
...
...
∗ ∗

























newcommand{BigFig}[1]{parbox{12pt}{Huge #1}}
newcommand{BigZero}{BigFig{0}}
$$
boldsymbol{A}=begin{pmatrix}
a_{11}&
vdots& BigZero
a_{1n}&
end{pmatrix},quad
boldsymbol{B}=begin{pmatrix}
0cdots 0& 1 & 0cdots 0
& 0 &
BigZero & vdots & BigZero
& 0 &
end{pmatrix}
$$

A =



a11
...
0a1n


 , B =





0 · · · 0 1 0 · · · 0
0
0
...
00





$$
boldsymbol{C}=
left( hspace{-arraycolsep}
begin{array}{cccc}
a&b & &
c&d &multicolumn{2}{c}{raisebox{1.5ex}[0pt]{BigZero}}
& &e&f
multicolumn{2}{c}{raisebox{1.5ex}[0pt]{BigZero}} & g &h
end{array}
right)
$$
C =




a b
c d 0
e f
0 g h




2 Ma trận khối
$$
W = left(
begin{array}{c:c}
begin{matrix}
S_n & U_n
V_n & S_n^mathrm{,t}
end{matrix} & text{Large{:0}}
hdashline %
text{rule{0pt}{17pt}Large{0}} & textit{Large{I}}
end{array}
right)
$$
W =



Sn Un
Vn S t
n
0
0 I




$$
left(
begin{array}{ccc:c}
&&&b
&mbox{smash{hugetextit{A}}}&&c
&&&d hdashline
e&f&g&h
end{array}
right)
$$




b
A c
d
e f g h




$$
left(
begin{array}{cccc|c}
&&&&b
&&&&c
&mbox{smash{Huge $A$}}&&&d
&&&&e hline
f&g&h&i&j
end{array}
right)
$$






b
c
A d
e
f g h i j






$$
arraycolsep5pt
left(
begin{array}{@{,}c|cccc@{,}}
a_{11}&a_{12}&a_{13}&a_{14}&a_{15}
hline
a_{21}&&&&
a_{31}&multicolumn{4}{c}{raisebox{-10pt}[0pt][0pt]{Huge $A$}}
a_{41}&&&&
a_{51}&&&&
end{array}

right)
$$






a11 a12 a13 a14 a15
a21
a31
Aa41
a51






defhsymb#1{mbox{strutrlap{smash{Huge$#1$}}quad}}
defhsymbu#1{smash{lower1.8exhbox{scalebox{4}{$#1$}}}}
begin{align*}
boldsymbol{A}
&=left(
begin{array}{ccccc}
1&a_{12}&a_{13}&a_{14}&a_{15}
1&a_{22}&a_{23}&a_{24}&a_{25}
1&a_{32}&a_{33}&a_{34}&a_{35}
1&a_{42}&a_{43}&a_{44}&a_{45}
1&a_{52}&a_{53}&a_{54}&a_{55}
end{array}
right)
&=left(
begin{array}{ccccc}
&a_{12}&a_{13}&a_{14}&a_{15}
&a_{22}&a_{23}&a_{24}&a_{25}
hsymbu{1}&a_{32}&a_{33}&a_{34}&a_{35}
&a_{42}&a_{43}&a_{44}&a_{45}
&a_{52}&a_{53}&a_{54}&a_{55}
end{array}
right)
end{align*}
$mathbf{1}=(1,1,1,1,1)’$
A =






1 a12 a13 a14 a15
1 a22 a23 a24 a25
1 a32 a33 a34 a35
1 a42 a43 a44 a45
1 a52 a53 a54 a55






=






a12 a13 a14 a15
a22 a23 a24 a25
1 a32 a33 a34 a35
a42 a43 a44 a45
a52 a53 a54 a55







1 = (1, 1, 1, 1, 1)
defhsymbu#1{smash{lower1.7exhbox{huge$#1$}}}
defhsymb#1{mbox{strutrlap{smash{Huge$#1$}}quad}}
$$
left(
begin{array}{c@{}c@{}c}
begin{array}{|cc|}
hline
a_{11} & a_{12}
a_{21} & a_{22}
hline
end{array}
& hsymb{0} & hsymb{0}
hsymbu{0} &
begin{array}{|ccc|}
hline
b_{11} & b_{12} & b_{13}
b_{21} & b_{22} & b_{23}
b_{31} & b_{32} & b_{33}
hline
end{array}
& hsymbu{0}
hsymbu{0} & hsymbu{0} &
begin{array}{|cc|}
hline
c_{11} & c_{12}
c_{21} & c_{22}
hline
end{array}
end{array}
right)
$$










a11 a12
a21 a22
0 0
0
b11 b12 b13
b21 b22 b23
b31 b32 b33
0
0 0
c11 c12
c21 c22










begin{equation*}
{boldsymbol{mathcal{H}}}_k =
left[

hspace{3pt}
begin{array}{ccccc}
cdashline{1-3}
multicolumn{1}{:c}{h_{k,1,0}(n)} & {h_{k,1,1}(n)}
&multicolumn{1}{c:}{h_{k,1,2}(n)} & {0} & {0}
cdashline{1-4}
{0} & multicolumn{1}{:c}{h_{k,1,0}(n-1)} & {h_{k,1,1}(n-1)}
&multicolumn{1}{c:}{h_{k,1,2}(n-1)} & {0}
cdashline{2-5}
{0} & {0} & multicolumn{1}{:c}{h_{k,1,0}(n-2)}
& {h_{k,1,1}(n-2)}& multicolumn{1}{c:}{h_{k,1,2}(n-2)}
cdashline{3-5}
end{array}
hspace{3pt}
right]_{12times 5}
end{equation*}

Hk =
























hk,1,0(n) hk,1,1(n) hk,1,2(n) 0 0
hk,2,0(n) hk,2,1(n) hk,2,2(n) 0 0
hk,3,0(n) hk,3,1(n) hk,3,2(n) 0 0
hk,4,0(n) hk,4,1(n) hk,4,2(n) 0 0
0 hk,1,0(n − 1) hk,1,1(n − 1) hk,1,2(n − 1) 0
0 hk,2,0(n − 1) hk,2,1(n − 1) hk,2,2(n − 1) 0
0 hk,3,0(n − 1) hk,3,1(n − 1) hk,3,2(n − 1) 0
0 hk,4,0(n − 1) hk,4,1(n − 1) hk,4,2(n − 1) 0
0 0 hk,1,0(n − 2) hk,1,1(n − 2) hk,1,2(n − 2)
0 0 hk,2,0(n − 2) hk,2,1(n − 2) hk,2,2(n − 2)
0 0 hk,3,0(n − 2) hk,3,1(n − 2) hk,3,2(n − 2)
0 0 hk,4,0(n − 2) hk,4,1(n − 2) hk,4,2(n − 2)
























12×5
$$
left[
begin{array}{c|c|cc}
a_{11} & a_{12} & cdots & a_{1n}
vdots & vdots & ddots & vdots hline
a_{i1} & a_{i2} & cdots & a_{in} hline
vdots & vdots & ddots & vdots
a_{n1} & a_{n2} & cdots & a_{nn}
end{array}
right]
$$








a11 a12 · · · a1n
...
...
...
...
ai1 ai2 · · · ain
...
...
...
...
an1 an2 · · · ann








3 Ma trận dạng đường chéo
$$
boldsymbol{A}=left(
begin{array}{ccccc}
a&&&&
&b&&&hsymb{0}
&&ddots&
&&&ddots&
hsymb{*}&&&&c

end{array}
right)
$$
A =








a
b 0...
...
∗ c








defhsymbl#1{smash{hbox{huge$#1$}}}
defhsymbu#1{smash{lower1.7exhbox{huge$#1$}}}
$$
A=
begin{pmatrix}
2 & 1 & & & hsymbu{0}
1 & 4 & ddots & &
& ddots & ddots & ddots &
& & ddots & 4 & 1
hsymbl{0} & & & 1 & 2
end{pmatrix}
$$
A =









2 1
0
1 4
...
...
...
...
... 4 1
0 1 2









$$
B=
begin{pmatrix}
ddots & & ddots & hsymbu{0}
& ddots & hsymbu{0} & ddots
ddots & hsymbl{0} & ddots &
hsymbl{0} & ddots & & ddots
end{pmatrix}
$$

B =








...
...
0...
0
...
... 0 ...
0 ...
...








Dùng với gói graphicx.sty
newcommandBpara[4]{%
begin{picture}(0,0)%
setlength{unitlength}{1pt}
put(#1,#2){rotatebox{#3}{raisebox{0mm}[0mm][0mm]{%
makebox[0mm]{$left. rule{0mm}{#4pt}right}$}}}}
end{picture}}
$$
begin{array}{ccccc}
a_{11}
a_{12} & a_{22}
a_{31} & a_{32} & a_{33}Bpara{0}{7}{61}{65}
a_{41} & a_{42} & a_{43} & a_{44}
a_{51} & a_{52} & a_{53}Bpara{-8}{-6}{-90}{58} & a_{54} &a_{55}
end{array}
$$
a11
a12 a22
a31 a32 a33



a41 a42 a43 a44
a51 a52 a53



a54 a55
newcommandSENB[4]{%
begin{picture}(0,0)%
setlength{unitlength}{1pt}
put(#1,#2){rotatebox{#3}{raisebox{-15pt}[0mm][0mm]{%
makebox[0mm]{rule{.5pt}{#4pt}}}}}
end{picture}}
$$
left(
begin{array}{ccccc}
hphantom{a_{11}} & a_{12} & a_{13} & a_{14} & a_{15}
* & & a_{23} & a_{24} & a_{25}
* & * && a_{35} & a_{35}
* & * & * & & a_{45}

* & * & * & * & SENB{-8}{8}{67}{120}
end{array}
right)
$$






a12 a13 a14 a15
∗ a23 a24 a25
∗ ∗ a35 a35
∗ ∗ ∗ a45
∗ ∗ ∗ ∗






$$
left(
begin{array}{ccccc}
& a_{12} & a_{13} & a_{14} & a_{15}
a_{21} & & a_{23} & a_{24} & a_{25}
a_{31} & a_{32} && a_{35} & a_{35}
a_{41} & a_{42} & a_{43} & & a_{45}
a_{51} & a_{52} & a_{53} & a_{54} & SENB{-8}{8}{67}{120}
end{array}
right)
$$






a12 a13 a14 a15
a21 a23 a24 a25
a31 a32 a35 a35
a41 a42 a43 a45
a51 a52 a53 a54






4 Chi tiết trong ma trận
1. Làm cột theo dấu chấm
$$
begin{Vmatrix}
begin{array}{rl}
269&1
11&92
5&25
end{array}
end{Vmatrix}
begin{Vmatrix}
begin{array}{r@{.}l@{%}}
269&1
11&92

5&25
end{array}
end{Vmatrix}
begin{Vmatrix}
begin{array}{r@{.}lr@{.}lr@{.}l}
3649&37 & 69&25 & -20&09
69&25 & 5&81 & 0&18
-20&09 & 0&18 & 1&00
end{array}
end{Vmatrix}
$$
269 1
11 92
5 25
269.1 %
11.92%
5.25%
3649.37 69.25 −20.09
69.25 5.81 0.18
−20.09 0.18 1.00
2. Dấu biên bao quanh
$$
Delta(s_{13},s_2)=
left{
S=begin{pmatrix}
0 & 0 & s_{13}
0 & s_2 & s_{23}
s_{13} & s_{23}& s_3
end{pmatrix}
vert ; s_{23},s_3in Z
right}
$$
∆(s13, s2) =



S =


0 0 s13
0 s2 s23
s13 s23 s3

 | s23, s3 ∈ ZZ



begin{align*}
nabla times overrightarrow{F}
& = left|
begin{array}{ccc}
widehat{i} & widehat{j} & widehat{k}
frac {partial }{partial x} & frac {partial }{partial y}
&frac{partial }{partial z}
F_x & F_y & F_z
end{array}
right|

& = left( frac {partial F_z}{partial y}

- frac {partial F_y} {partial z} right) widehat{i}
+ left( frac{partial F_x} {partial z}
-frac {partial F_z} {partial x} right) widehat{j}
+left( frac {partial F_y} {partial x}
- frac {partial F_x} {partial y} right) widehat{k}
end{align*}
×
−→
F =
i j k
∂
∂x
∂
∂y
∂
∂z
Fx Fy Fz
=
∂Fz
∂y
−
∂Fy
∂z
i +
∂Fx
∂z
−
∂Fz
∂x
j +
∂Fy
∂x
−
∂Fx
∂y
k
5 Các móc biên
1. Tính toán trên dòng
begin{alignat*}{2}
&
begin{pmatrix}
1 & 2 & 1 &vdots & 1 & 0 & 0 [-3pt]
2 & 1 & 1 &vdots & 0 & 1 & 0 [-3pt]
1 & 1 & 1 &vdots & 0 & 0 & 1
end{pmatrix}
&
qquad
&
left{
begin{array}{l}
(1)[5pt]
(2)[5pt]
(3)
end{array}
right.
intertext{Cần tính}
&
begin{pmatrix}
1 & 2 & 1 &vdots & 1 & 0 & 0 [-3pt]
0 &-3 &-1 &vdots &-2 & 1 & 0 [-3pt]
1 &-1 & 1 &vdots &-1 & 0 & 1
end{pmatrix}
&
qquad
&

left{
begin{array}{l}
(1)[5pt]
(2)=(2)-2times (1)[5pt]
(3)=(3)-(1)
end{array}
right.
end{alignat*}




1 2 1
... 1 0 0
2 1 1
... 0 1 0
1 1 1
... 0 0 1







(1)
(2)
(3)
Cần tính




1 2 1
... 1 0 0
0 −3 −1
... −2 1 0
1 −1 1
... −1 0 1







(1)
(2) = (2) − 2 × (1)
(3) = (3) − (1)
2. Dùng overbrace trên ma trận
begin{equation}
mathbf{A}
=left{a_{pq}right}
=begin{array}{c}
overbrace{hspace{4.75cm}}^{L_B=0,1,2ldots,4}
left(begin{array}{ccccc}
a_{00} & a_{01} & a_{02} & a_{03} & a_{04}
a_{10} & a_{11} & a_{12} & a_{13} & a_{14}
a_{20} & a_{21} & a_{22} & a_{23} & a_{24}
a_{30} & a_{31} & a_{32} & a_{33} & a_{34}
a_{40} & a_{41} & a_{42} & a_{43} & a_{44}
end{array}
right)
end{array}
end{equation}
A = {apq} =
LB=0,1,2...,4






a00 a01 a02 a03 a04
a10 a11 a12 a13 a14
a20 a21 a22 a23 a24
a30 a31 a32 a33 a34
a40 a41 a42 a43 a44






(1)

begin{equation}
underbrace{
begin{pmatrix}
tilde{C}_{11} & cdots &tilde{C}_{1n} &1
vdots & ddots & vdots &vdots
tilde{C}_{n1} & cdots &tilde{C}_{nn} &1
1 & cdots & 1 & 0
end{pmatrix}}_{(n+1)times(n+1)}
end{equation}





˜C11 · · · ˜C1n 1
...
...
...
...
˜Cn1 · · · ˜Cnn 1
1 · · · 1 0





(n+1)×(n+1)
(2)
3. Dùng gói lệnh bigdelim.sty multirow.sty
$$
begin{array}{rrcccccl}
&&multicolumn{5}{c}{overbrace{hspace{3.5em}}^{3}
overbrace{hspace{2.5em}}^{2}}&
ldelim{{2}{14pt}[2]&
ldelim({4}{14pt}[] &1 &2 &3 &4 &5 &rdelim){4}{14pt}[]
& &1 &0 &0 &0 &0 &
ldelim{{2}{14pt}[2]& &0 &1 &0 &0 &0 &
& &0 &0 &1 &0 &0 &
end{array}
$$
3 2
2




1 2 3 4 5




1 0 0 0 0
2
0 1 0 0 0
0 0 1 0 0
6 Cột và hàng ngoài ma trận
1. dùng gói lệnh blkarray.sty ngoài matrân bên phải và dưới
newcommandbigstrutht{vrule width0pt height 12pt depth0ptrelax}
newcommandbigstrutdp{vrule width0pt height 0pt depth5ptrelax}
$$

begin{blockarray}{*{4}{c}}
begin{block}{[ccc]c}
bigstrutht 1-lambda x & 0 & 0 & ell_1
0 & 1-lambda x & 0 & ell_2
bigstrutdp 0 & 0 & 1-lambda x & ell_3
end{block}
c_1 & c_2 & c_3
end{blockarray}
$$




1 − λx 0 0 1
0 1 − λx 0 2
0 0 1 − λx 3
c1 c2 c3
2. Kẻ trong và cột ngoài
$$
begin{array}{crcc|cl}
& &e &multicolumn{1}{c}{f}&g &
a&ldelim[{4}{5pt}[]&x &x &x &rdelim]{4}{5pt}[]
b& &x &x &x &
& &cdots&cdots &cdots&
c& &x &x &x &
end{array}
$$
e f g
a




x x x




b x x x
· · · · · · · · ·
c x x x
$$
begin{blockarray}{ccccc}
& e & f & &g
begin{block}{c[cccc]}
a & x & x & vert & x
b & x & x & vert & x
& cdots & cdots & cdots & cdots
c & x & x & vert & x
end{block}
end{blockarray}
$$

e f g






a x x | x
b x x | x
· · · · · · · · · · · ·
c x x | x
$$
bordermatrix{
&e&f&&gcr
a&x&x&vert&xcr
b&x&x&vert&xcr
&cdots&cdots&cdots&cdotscr
c&x&x&vert&xcr
}
$$




e f g
a x x | x
b x x | x
· · · · · · · · · · · ·
c x x | x




$$
begin{array}{c@{}cc}
& begin{array}{ccc}e & f & gend{array}
begin{array}{c}abcend{array} &
left[begin{array}{cc|c}
x & x & x
x & x & x
hdotsfor{3}
x & x & x
end{array}right]
end{array}
$$
e f g
a
b
c




x x x
x x x
. . . . . . . .
x x x




3. Dùng bigdelim.sty

$$
begin{array}{rrcccll}
& &1&2&3& &
1&ldelim({3}{3mm}[] &a&b&c& rdelim){3}{3mm}[]&1
2& &d&e&f& &2
3& &g&h&i& &3
& &1&2&3& &
end{array}
$$
1 2 3
1


a b c


1
2 d e f 2
3 g h i 3
1 2 3
$$
& &1&2&3& &
1&ldelim[{3}{3mm}[] &a&b&c& rdelim]{3}{3mm}[]&1
2& &d&e&f& &2
3& &g&h&i& &3
& &1&2&3& &
end{array}
$$
1 2 3
1


a b c


1
2 d e f 2
3 g h i 3
1 2 3
$$
& &1&2&3& &
1&ldelim{{3}{3mm}[] &a&b&c& rdelim}{3}{3mm}[]&1
2& &d&e&f& &2
3& &g&h&i& &3
& &1&2&3& &
end{array}
$$

1 2 3
1



a b c



1
2 d e f 2
3 g h i 3
1 2 3
4. Ma trận và gói lệnh graphicx.sty
defrb#1{rotatebox{90}{$xleftarrow{#1}$}}
begin{tabular}{c}
$begin{matrix}
rb{text1}&rb{text1}&rb{text1}&rb{text1}
end{matrix}$
$begin{bmatrix}
X_x & Y_x & Z_x & T_x
X_y & Y_y & Z_y & T_y
X_z & Y_z & Z_z & T_z
0 & 0 & 0 & 1
end{bmatrix}$
end{tabular}
text1
←−−−
text1
←−−−
text1
←−−−
text1
←−−−




Xx Yx Zx Tx
Xy Yy Zy Ty
Xz Yz Zz Tz
0 0 0 1




5. Một phần tử là khối
$$
begin{pmatrix}
x & x & x & x
x & x & x & x
x & x & x & x
begin{matrix}x + y + {}[-2pt] z + a end{matrix}
& x & x & x
end{pmatrix}
$$





x x x x
x x x x
x x x x
x + y +
z + a x x x






$$
begin{pmatrix}
x & x & x & x
x & x & x & x
x & x & x & x
begin{matrix}x + y + z + a end{matrix}
& x & x & x
end{pmatrix}
$$






x x x x
x x x x
x x x x
x + y+
z + a
x x x






7 Định nghĩa Matrix mới
$
bordermatrix{
& a & a & a cr
a & a & b & c cr
a & x & y & z
}
$
hfill
$
bordermatrix[{[]}]{
& 1 & 2 & 3 cr
1 & a & b & c cr
2 & x & y & z
}
$
hfill
$
bordermatrix[{}]{
& 1 & 2 & 3 cr
1 & a & b & c cr
2 & x & y & z
}
$
a a a
a a b c
a x y z
1 2 3
1 a b c
2 x y z
1 2 3
1 a b c
2 x y z

$
bordermatrix*{
a & b & c & 1cr
x & y & z & 2cr
1 & 2 & 3 &
}
$
hfill
$
bordermatrix*[{[]}]{
a & b & c & 1cr
x & y & z & 2cr
1 & 2 & 3 &
}
$
hfill
$
bordermatrix*[{}]{
a & b & c & 1cr
x & y & z & 2cr
1 & 2 & 3 &
}
$
a b c 1
x y z 2
1 2 3
a b c 1
x y z 2
1 2 3
a b c 1
x y z 2
1 2 3
8 Hệ phương trình
$$
bordermatrix{ & A_1 & A_2 & cdots & A_n cr
C_1 & w_1 & w_2 & ldots & w_1 cr
C_2 & w_2 & w_2 & ldots & w_2 cr
vdots & vdots & vdots & ddots & vdots cr
C_n & w_n & w_n & ldots & w_n cr
}
bordermatrix{ & cr
&w_1 cr
&w_2 cr
&vdots cr
&w_n cr
}
=n
bordermatrix{ & cr

&w_1 cr
&w_2 cr
&vdots cr
&w_n cr
}
$$
$$
bordermatrix{ &A_1 & A_2 & ldots & A_3 cr
&w1/w1 & w1/w1 & ldots & w1/w1cr
&w2 & w2 & ldots & w2cr
&vdots & vdots & vdots & vdots cr
&w3 & w3 & ldots & w3 cr
}
$$





A1 A2 · · · An
C1 w1 w2 . . . w1
C2 w2 w2 . . . w2
...
...
...
...
...
Cn wn wn . . . wn










w1
w2
...
wn





= n





w1
w2
...
wn









A1 A2 . . . A3
w1/w1 w1/w1 . . . w1/w1
w2 w2 . . . w2
...
...
...
...
w3 w3 . . . w3




9 Chú thích bên phải
$$
begin{array}{rcccccll}
ldelim({7}{4mm}[] & x_{11} & x_{12} & dots & x_{1p}
&rdelim){7}{4mm}[]& rdelim}{4}{3.25cm}[some text]
&x_{21} & x_{22} & dots & x_{2p} &&
& &vdots && &&
&x_{n_1 1}& x_{n_1 2} & dots & x_{n_1 p}&&
&x_{n_1+1,1}&x_{n_1+1,2} & dots
& x_{n_1+1, p} &&rdelim}{3}{3.25cm}[some more text]
& &vdots && &&
&x_{n_1+n_2, 1} & x_{n_1+n_2,2} & dots & x_{n_1+n_2,p}&&
end{array}
$$











x11 x12 . . . x1p













some text
x21 x22 . . . x2p
...
xn11 xn12 . . . xn1p
xn1+1,1 xn1+1,2 . . . xn1+1,p



some more text...
xn1+n2,1 xn1+n2,2 . . . xn1+n2,p
$$
left(
begin{array}{ccccc}
x_{11} & x_{12} & dots & x_{1p}
x_{21} & x_{22} & dots & x_{2p}
&vdots &&
x_{n_1 1}& x_{n_1 2} & dots & x_{n_1 p}
x_{n_1+1,1}&x_{n_1+1,2} & dots & x_{n_1+1, p}
&vdots &&
x_{n_1+n_2, 1} & x_{n_1+n_2,2} & dots & x_{n_1+n_2,p}
end{array}
right)
$$












x11 x12 . . . x1p
x21 x22 . . . x2p
...
xn11 xn12 . . . xn1p
xn1+1,1 xn1+1,2 . . . xn1+1,p
...
xn1+n2,1 xn1+n2,2 . . . xn1+n2,p












begin{equation*}
begin{pmatrix}
01&02&03&04&05&06&07&08&09&10&11&12&13&14
01&02&03&hdotsfor{7}&11&12&13&14
end{pmatrix}
end{equation*}
01 02 03 04 05 06 07 08 09 10 11 12 13 14
01 02 03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 13 14
begin{equation*}
begin{pmatrix}

01&02 &03&04&05&06&07&08&09&10&11&12&13&14
02&02 &03&04&05&06&07&08&09&10&11&12&13&14
03&ldots &03&04&05&06&07&08&09&10&11&12&13&14
04&hdotsfor{2} &04&05&06&07&08&09&10&11&12&13&14
05&hdotsfor{3} &05&06&07&08&09&10&11&12&13&14
06&hdotsfor{4} &06&07&08&09&10&11&12&13&14
07&hdotsfor{5} &07&08&09&10&11&12&13&14
08&hdotsfor{6} &08&09&10&11&12&13&14
09&hdotsfor{7} &09&10&11&12&13&14
10&hdotsfor{8} &10&11&12&13&14
11&hdotsfor{9} &11&12&13&14
12&hdotsfor{10}&12&13&14
13&hdotsfor{11}&13&14
14&hdotsfor{12}&14
end{pmatrix}
end{equation*}
























01 02 03 04 05 06 07 08 09 10 11 12 13 14
02 02 03 04 05 06 07 08 09 10 11 12 13 14
03 . . . 03 04 05 06 07 08 09 10 11 12 13 14
04 . . . . . . . 04 05 06 07 08 09 10 11 12 13 14
05 . . . . . . . . . . . . 05 06 07 08 09 10 11 12 13 14
06 . . . . . . . . . . . . . . . . 06 07 08 09 10 11 12 13 14
07 . . . . . . . . . . . . . . . . . . . . . 07 08 09 10 11 12 13 14
08 . . . . . . . . . . . . . . . . . . . . . . . . . 08 09 10 11 12 13 14
09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 09 10 11 12 13 14
10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 12 13 14
11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 13 14
12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 13 14
13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 14
14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

























Bigdelim help

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (11)

Destaque

Destaque (6)

Semelhante a Bigdelim help

Semelhante a Bigdelim help (20)

Mais de Mai Mẫn Tiệp

Mais de Mai Mẫn Tiệp (20)

Último

Último (20)

Bigdelim help