Báo cáo Matlab: Đại số tuyến tính

H C QU C GIA THÀNH PH

H

CHÍ MINH

I H C BÁCH KHOA
N-

NT

__________________§§§__________________

BÁO CÁO MATLAB
IS

TUY N TÍNH

L P: DD16LT11
GVHD: NGUY N XUÂN M

Tp H Chí Minh ,

6


Danh sách thành viên nhóm:

STT

H VÀ TÊN

1

MSSV
1612562

2

Võ Nh t Ti n

1613551

3

Nguy n An Bình

1610235

4

cM n

1611998

5

Nguy n Chí Tâm

1613053

6

Nguy n Lê Huy n Trân

1613676

7

Ti

t

1610624

8

Bùi H u Bình

1610225

9

Nguy n Chánh L c

1652363

10

Phan Thanh Thi n

1613330


1.1: L nh real:................................................................................................................ 4
1.2: L nh Imag:.............................................................................................................. 4
1.3: L nh abs: ................................................................................................................ 4
1.4: L nh angle: ............................................................................................................. 5
1.5: L nh conj: ............................................................................................................... 5
PH N II: CÁC L NH TRONG MA TR N:

2.1: L nh det: ................................................................................................................. 5
2.2: L nh diag: ............................................................................................................... 6
2.3: L nh eig: ................................................................................................................. 6
2.4: L nh eye:................................................................................................................. 7
2.5: L nh inv: ................................................................................................................. 7
mpty : ........................................................................................................ 8
2.7: L nh length: ............................................................................................................ 8
2.8: L nh linspace: ......................................................................................................... 9
2.9: L nh ones:............................................................................................................... 9
2.10: L nh pascal: .......................................................................................................... 9
2.11: L nh rank: ........................................................................................................... 10
2.12: L nh reshape:...................................................................................................... 10
2.13: L nh size:............................................................................................................ 10


2.14: L nh tril: ............................................................................................................. 11
2.15: L nh triu:............................................................................................................. 11
2.16: L nh zeros:.......................................................................................................... 12
2.17: L nh [Q, R]=qr(A):............................................................................................. 12
PH N III: CÁC L NH TRONG KHÔNG GIAN VECTO :

3.1: Lênh norm :........................................................................................................... 13
3.2: L nh dot( ):.......................................................................................................... 14
3.3: L nh cross : ......................................................................................................... 14
3.4: L nh [v,d]=eig(x):................................................................................................. 15
3.5: L nh max(X):........................................................................................................ 16
3.6: L nh min:.............................................................................................................. 16


PH N I: CÁC L NH TRONG S PH C:
ph c. i2 hay j2 b ng -1.
1.1: L nh real:
n th c c a s ph c.
Cú pháp: real(x)
Ví d : z=1+2i;
phanthuc=real(z)
phanthuc=1.
1.2: L nh Imag:
nh xu t ra ph n o c a s ph c.
Cú pháp: imag(x)
VD:z=1+2i;
phanao=imag(z)
phanao=2.
1.3: L nh abs:
nh xu t ra modun c a s ph c.
Cú pháp: abs(x)
VD: z=1+2i;
Z1=abs(z)

Z1=2.2360
1.4: L nh angle:
Tìm Agument c a s ph c.
Cú pháp: angle(x)=
VD: z=1+2i;
Argument=angle(z)
Argument=1.1071
1.5: L nh conj:
ng liên hi p c a s ph c.
Cú pháp: conj(x)
VD: conj(2+3i)
Ans= 2-3i

PH N II: CÁC L NH TRONG MA TR N:
2.1: L nh det:
nh th c ma tr n vuông A
Cú pháp: det(x)
VD: A=[1 2 3; 3 4 5; 4 5 6];
det(A)


ans= 0
2.2: L nh diag:
o ma tr n chéo v i các ph n t
p

c

Cú pháp: diag(x)
VD:z=[1 5 7]

diag(z)
ans =
1

0

0

0

5

0

0

0

7

2.3: L nh eig:
t giá tr riêng cho ma tr n A.
Cú pháp: eig(x)
VD:
a=[-1 2 3;1 0 3;-1 5 5]
a=
-1

2

3

1

0

3

ng chéo là các


-1

5

5

eig(a)
ans =
-2.0000
-1.0000
7.0000
2.4: L nh eye:
o ma tr

c

c.

Cú pháp: eye(n)

VD:
eye(2)
ans = 1
0

0
1

2.5: L nh inv:
n ng

o c a ma tr n A

Cú pháp: inv(A)
VD: >> A=[1 2 3;1 2 6;6 8 4];
>> inv(A)


ans =
-3.3333

1.3333

0.5000

2.6667

-1.1667

-0.2500

-0.3333

0.3333

-0.0000

2.6

:
n 0 hay không.

Cú pháp: isempty(A)
VD: a=[1 2;3 4]
a=
1

2

3

4

isempty(a)
ans =
0
2.7: L nh length:
dài c
Cú pháp: length(v)
VD: >> v=[1 2 3];

>> length(v)
ans = 3
2.8: L nh linspace:
n nh .
Cú pháp: linspace(a,b,n)
VD: linspace(2,5,3)
ans = 2.0000

3.5000

5.0000

2.9: L nh ones:
o ma tr n c

u có các ph n t b ng 1

Cú pháp: ones(n)
VD: >> ones(2)
ans =

1

1

1

1

2.10: L nh pascal:
o ma tr n pascal c p n.
Cú pháp: pascal(n)
VD:>> pascal(2)
ans =
1

1


1

2

2.11: L nh rank:
ng c a ma tr n A.
Cú pháp: rank(A)
VD: >> A=[1 2 4; 3 5 6;2 3 5];
>> rank(A)
ans = 3
2.12: L nh reshape:
i kích c ma tr n.
Cú pháp: reshape(A,m,n)
VD: >> A=[1 2 3;4 5 6];
>> reshape(A,3,2)
ans =
1

5

4

3

2

6

2.13: L nh size:
ma tr n A.
Cú pháp: size(A)


VD: >> A=[1 2 3; 3 45 5];
>> size(A)
ans = 2

3

2.14: L nh tril:
: Trích ra ma tr

i t ma tr n A.

Cú pháp: tril(A)
VD: >> a=[1 3 5; 2 4 5; 13 54 3]
>> tril(a)
ans =

1

0

0

2

4

0

13

54

3

2.15: L nh triu:
n tam giác trên t ma tr n A.
Cú pháp: triu(A)
VD: >>
a=[1 3 5; 2 4 5; 13 54 3];


>> triu(a)

ans =

1

3

5

0

4

5

0

0

3

2.16: L nh zeros:
o ma tr n 0 c p n.
Cú pháp: zeros(n)
VD: >> zeros(2)
ans =
0

0

0

0

2.17: L nh [Q, R]=qr(A):
n A thành tích hai ma tr n Q và R.
Cú pháp: [Q, R]=qr(A)
VD: >> a=[1 3 4; 4 5 3; 4 5 2];
>> [Q,R]=qr(a)
Q=
-0.1741
-0.6963

0.9847
-0.1231

-0.0000
-0.7071


-0.6963
R=

-0.1231

-5.7446

0.7071

-7.4853

-4.1779

0

1.7233

3.3235

0

0

-0.7071

PH N III: CÁC L NH TRONG KHÔNG GIAN
VECTO :
3.1: Lênh norm :
ra giá tr
Cú pháp : v= norm(v)

Vd: v=[40 , 30]

V=norm(v)

V= 50

i s cho 1 vecto


3.2: L nh dot( ):

ra giá tr

ng c a hai vecto

Cú pháp : v=dot(A,B)

Vd : A=[1 ,3 ,5]; B=[2 ,2 ,1]

V=dot(A,B)

V= 13

3.3: L nh cross :

ra giá tr

Cú pháp : cross(A,B)

>> A=[1;2;3];

>> B=[4;5;6];

>> cross(A,B)

ans =

ng c a hai vecto


-3

6

-3

3.4: L nh [v,d]=eig(x):
t giá tr

a ma tr n A, chéo hóa

ma tr n.
Cú pháp: [v,d]=eig(x)
Vd:
[v,d]=eig(a)
v=
-0.0816

-0.6396

0.4082

-0.8165

-0.6396

0.4082

0.5715

0.4264

0.8165

-2.0000

0

0

-1.0000

0

d=

0
0

0

7.0000


3.5: L nh max(X):
v giá tr l n nh
Cú pháp: max(X)
VD: >> x=[1 2 4 5];
>> max(x)
ans = 5
3.6: L nh min:
v giá tr nh nh
Cú pháp: min(X)

VD: >> x=[1 2 4 5];
>> min(x)
ans=1