, , . , , ones, zeros, sum, cat, size, ndims, reshape . , () , .. , , 2.15 eye rand.
, , sum prod, ,
>> A=[2 2 2; 3 3 3; 5 5 5]
A =
2 2 2
3 3 3
5 5 5
>> prod(A)
ans =
30 30 30
, sum prod . , , . , , : 1 ( ), 2 . :
>> A=[1 2; 3 4]
A =
1 2
3 4
>> sum(A,2)
ans =
max min . , , , ,
>> x=[3 7 5 4.8 8.95 2 6];
>> min(x)
ans =
>> max(x)
ans =
8.9500
>> A=[1 2 3; 4 5 6; 7 8 9]
A =
1 2 3
4 5 6
7 8 9
>> max(A)
ans =
7 8 9
>> min(A)
ans =
1 2 3
, , max min :
>> max(A,[],2)
ans =
>> min(A,[],2)
ans =
, -.
sort , .
>> b=[3 2 4 8 5 7 3 1 0]
b =
3 2 4 8 5 7 3 1 0
>> sort(b)
ans =
0 1 2 3 3 4 5 7 8
>> B=[3 7 9; 4 8 1; 2 9 5]
B =
3 7 9
4 8 1
2 9 5
>> sort(B,2)
ans =
3 7 9
1 4 8
2 5 9
sort . , , :
>> [B,ind]=sort(B,2)
B =
3 7 9
1 4 8
2 5 9
ind =
1 2 3
3 1 2
1 3 2
4.
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, MATLAB () / \. .
\ , A B A\B, inv(A)*B, inv(A) , A.
/ . A/B B*inv(A), .. , , Y*A=B.
.
, .
MATLAB :
cond(A) A ( , );
condeig(A) , A;
rcond(A) A (, , , );
det(A) () A;
rank(A) A;
norm(A) A (
);
trace(A) , , ;
orth(A) A [20,21,27,40,45,46,51,95,96,117-120,134,135,238];
rref(A) n- [E v], E n- , v -, ;
rrefmovie(A) , rref, ;
inv(A) ( ( ); A, A );
pinv(A) ( A P ( A) A*P*A=A P*A*P=P (, ));
chol(A) ( ) A, .. T , T*T=A;
lu(A) LU- A ( ; [L,U]=lu(A), (U), (L), A=L*U; [L,U,P]=lu(A) , P*A=L*U);
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qr(A) QR- A ( );
d=eig(A) d, () ( ) A;
[V,D]=eig(A) V ( ) D ( (, A); A), .., , ( , ) A*V=V*D;
s=svd(A) , ( );
[U,S,V]=svd(A) S ( S U ( U , A*A') V ( V , A*A'), , A=U*S*V;
[U,T]=shur(A) () U T ( T A), , A=U*T*U';
[V,J]=jordan(A) A, J A; V , .
MATLAB cdf2rdf, hess, qz rsf2csf . m, , expm, logm sqrtm, exp, log, sqrt, , , .
:
>> A=[2 -3 1; 1 2 -6; 5 1 1];
>> cond(A)
ans =
2.4374
>> det(A)
ans =
>> rank(A)
ans =
>> [V,D]=eig(A)
V =
-0.6085 + 0.0000i 0.1224 + 0.3873i 0.1224 - 0.3873i
0.6172 + 0.0000i 0.7355 + 0.0000i 0.7355 + 0.0000i
-0.4988 + 0.0000i 0.3184 - 0.4390i 0.3184 + 0.4390i
D =
5.8626 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.4313 + 4.1075i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i -0.4313 - 4.1075i
(Ax=0). , , () , . , , , . n-r. null, :
Z=null(A) Z, ;
Z=null(A,r) Z, ;
Az=0.
, , ( , ), , . , . MATLAB , . , , sparse:
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>> A=[0 1 0 0; 0 0 1 0; 0 0 0 1; -4 0 0 0]
A =
0 1 0 0
0 0 1 0
0 0 0 1
-4 0 0 0
>> S=sparse(A)
S =
(4,1) -4
(1,2) 1
(2,3) 1
(3,4) 1
>> whos S
Name Size Bytes Class Attributes
S 4x4 104 double sparse
>> whos A
Name Size Bytes Class Attributes
A 4x4 128 double
, sparse , S sparse array, , A.
full:
>> full(S)
ans =
0 1 0 0
0 0 1 0
0 0 0 1
-4 0 0 0
, MATLAB , , , [70].