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### use SVD to find left inverse?

I'm trying some basic linear algebra function. I want to solve a singular matrix which is not easy to get inverse matrix.

for example, I have

A = [-1, 0, 0, 0, 1, 0, 0, 0; 0, -1, 0, 0, 0, 1, 0, 0]

since is non-inevitable, we should use SVD to get the inverse.

I try this code (skiped the steps to assign value to A)

    Mat inverse= (A).inv(DECOMP_SVD);

cout << "A * inverse = " <<  inverse*A << endl;
cout << "inverse * A = " << A*inverse << endl;


and the outputs would be

A * inverse =

[0.5, 0, 0, 0, -0.5, 0, 0, 0;

0, 0.5, 0, 0, 0, -0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

-0.5, 0, 0, 0, 0.5, 0, 0, 0;

0, -0.5, 0, 0, 0, 0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0]

inverse * A =

[1, 0;

0, 1]

(good)

so the left inverse not equal to the right inverse. However in the function I can just get the right one. How should I get the left one?

### use SVD to find left inverse?

I'm trying some basic linear algebra function. I want to solve a singular matrix which is not easy to get inverse matrix.

for example, I have

A = [-1, 0, 0, 0, 1, 0, 0, 0; 0, -1, 0, 0, 0, 1, 0, 0]

since is non-inevitable, we should use SVD to get the inverse.

I try this code (skiped the steps to assign value to A)

    Mat inverse= (A).inv(DECOMP_SVD);

cout << "A * inverse = " <<  inverse*A A*inverse << endl;
cout << "inverse * A = " << A*inverse  inverse*A << endl;


and the outputs would be

A * inverse =

[0.5, 0, 0, 0, -0.5, 0, 0, 0;

0, 0.5, 0, 0, 0, -0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

-0.5, 0, 0, 0, 0.5, 0, 0, 0;

0, -0.5, 0, 0, 0, 0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0]

inverse * A =

[1, 0;

0, 1]

(good)

so the left inverse not equal to the right inverse. However in the function I can just get the right one. How should I get the left one?

### use SVD to find left inverse?

I'm trying some basic linear algebra function. I want to solve a singular matrix which is not easy to get inverse matrix.

for example, I have

A = [-1, 0, 0, 0, 1, 0, 0, 0; 0, -1, 0, 0, 0, 1, 0, 0]

since is non-inevitable, we should use SVD to get the inverse.

I try this code (skiped the steps to assign value to A)

    Mat inverse= (A).inv(DECOMP_SVD);

cout << "A * inverse = " <<  A*inverse << endl;
cout << "inverse * A = " <<  inverse*A << endl;


and the outputs would be

A * inverse =

[0.5, 0, 0, 0, -0.5, 0, 0, 0;

0, 0.5, 0, 0, 0, -0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

-0.5, 0, 0, 0, 0.5, 0, 0, 0;

0, -0.5, 0, 0, 0, 0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0]

inverse * A =

[1, 0;

0, 1]

(good)

so the left inverse not equal to the right inverse. However in the function I can just get the right one. How should I get the left one?

### use SVD to find left inverse?

I'm trying some basic linear algebra function. I want to solve a singular matrix which is not easy to get inverse matrix.

for example, I have

A = [-1, 0, 0, 0, 1, 0, 0, 0; 0, -1, 0, 0, 0, 1, 0, 0]

since is non-inevitable, we should use SVD to get the inverse.

I try this code (skiped the steps to assign value to A)

    Mat inverse= (A).inv(DECOMP_SVD);

cout << "A * inverse = " <<  A*inverse << endl;
cout << "inverse * A = " <<  inverse*A << endl;


and the outputs would be

A * inverse =

[0.5, 0, 0, 0, -0.5, 0, 0, 0;

0, 0.5, 0, 0, 0, -0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

-0.5, 0, 0, 0, 0.5, 0, 0, 0;

0, -0.5, 0, 0, 0, 0.5, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 0]