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

Recommended

Recommended

More Related Content

What's hot

What's hot (11)

Viewers also liked

Viewers also liked (6)

Similar to Bigdelim help

Similar to Bigdelim help (20)

More from Mai Mẫn Tiệp

More from Mai Mẫn Tiệp (20)

Recently uploaded

Recently uploaded (20)

Bigdelim help