Singular value decomposition

Singular value decomposition
You are encouraged to solve this task according to the task description, using any language you may know.

$A$ is any m by n matrix, square or rectangular. Its rank is r. We will diagonalize this A, but not by Failed to parse (syntax error): {\displaystyle X^{−1}AX} . The eigenvectors in $X$ have three big problems: They are usually not orthogonal, there are not always enough eigenvectors, and $Ax$ = Failed to parse (syntax error): {\displaystyle λx} requires $A$ to be a square matrix. The singular vectors of $A$ solve all those problems in a perfect way.

The Singular Value Decomposition (SVD)

According to the web page above, for any rectangular matrix $A$, we can decomposite it as Failed to parse (syntax error): {\displaystyle A=UΣV^T}

Task Description

Firstly, input two numbers "m" and "n".

Then, input a square/rectangular matrix $A^{m\times n}$.

Finally, output Failed to parse (syntax error): {\displaystyle U,Σ,V} with respect to $A$.

Example

Sample Input

2 2
3 0
4 5

From the input above we can know that $A$ is a 2 by 2 matrix.

Sample Output

   
0.31622776601683794 -0.9486832980505138
0.9486832980505138 0.31622776601683794

6.708203932499369 0
0 2.23606797749979

0.7071067811865475 -0.7071067811865475
0.7071067811865475 0.7071067811865475

The output may vary depending your choice of the data types.