Matrix inverse with svd

Question

Elie Hatem 2021-6-7

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/850160-matrix-inverse-with-svd

评论： Arnab Paul 2023-10-27

采纳的回答： Christine Tobler

在 MATLAB Online 中打开

Hello,

I am trying to invert a matrix using svd and \ and comparing the result with inv().

For this matrix:

A = [ 2 4 6; 8 5 7 ; 0 3 1]

I did the svd decomposition as follows:

[U,S,V] = svd(A);

And, I believe the inverse of A can be expressed as :

So, I tried it by writing the code below:

disp('inverse with svd:')
disp(V*S\U')

And, I got this answer:

inverse with svd:
0236    0.0440   -0.0528
1765    0.1361    0.1922
4277   -0.3787   -0.1247

Then, I tried to invert A using inv() as follows:

disp('inverse with inv:')
disp(inv(A))

However, I got a different answer as seen below:

inverse with inv:
   -0.2000    0.1750   -0.0250
   -0.1000    0.0250    0.4250
    0.3000   -0.0750   -0.2750

Can someone tell me what I am doing wrong?

My main goal is that I want to use svd to invert large matrices that may be close to becoming singular.

Thank you

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Answer 1

Christine Tobler 2021-6-7

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/850160-matrix-inverse-with-svd#answer_719155

在 MATLAB Online 中打开

Use one of

A = [ 2 4 6; 8 5 7 ; 0 3 1]
A = 3×3
     2     4     6
     8     5     7
     0     3     1
[U,S,V] = svd(A);
V*inv(S)*U'
ans = 3×3
   -0.2000    0.1750   -0.0250
   -0.1000    0.0250    0.4250
    0.3000   -0.0750   -0.2750
V*(S\U')
ans = 3×3
   -0.2000    0.1750   -0.0250
   -0.1000    0.0250    0.4250
    0.3000   -0.0750   -0.2750
% The formula you're using above puts the parentheses in a different place
% than you think:
V*S \ U'
ans = 3×3
    0.0236    0.0440   -0.0528
    0.1765    0.1361    0.1922
    0.4277   -0.3787   -0.1247
(V*S) \ U'
ans = 3×3
    0.0236    0.0440   -0.0528
    0.1765    0.1361    0.1922
    0.4277   -0.3787   -0.1247