Find the symmetric and skew-symmetric matrices by 2x2 blocks

Hello everyone,

I need to extract from 2n by 2n matrix the symetric and skew-symetric 2x2 blocks:

For example, for given A:

A=[
    0,-1,  2,3;
    1,0,   4,2;
    -2,3,   0,-1;
    4,-2,  1,0;
    ]

I want to get:

A_symetric= [
    0,-1,  0,3;
    1,0,   4,0;
    0,3,   0,-1;
    4,0,  1,0;
    ]

And

A_skew_symetric= [
    0,0,  2,0;
    0,0,  0,2;
    -2,0, 0,0;
    0,-2, 0,0;
    ]

[Matt J]

It is unclear why you consider A_symmetric to be blockwise symmetric. The 2x2 submatrix

0,3,

4,0,

is not symmetric.

Answer 1

[Matt J]

A=[
    0,-1,  2,3;
    1,0,   4,2;
    -2,3,   0,-1;
    4,-2,  1,0;
    ];

n=length(A)/2;

mask = (-1).^( (1:2*n).' + (1:2*n) )==-1;

A_symetric=A.*(mask)

A_symetric = 4×4

0 -1 0 3 1 0 4 0 0 3 0 -1 4 0 1 0

A_skew_symmetric=A.*(~mask)

A_skew_symmetric = 4×4

0 0 2 0 0 0 0 2 -2 0 0 0 0 -2 0 0

●

[Ohad Shapira]

In a simple change this solution does not hold...

A=[

5,-1, 2,3;

1,5, 4,2;

-2,3, 5,-1;

4,-2, 1,5;

];

I get:

A_skew_symmetric =

5 0 2 0

0 5 0 2

-2 0 5 0

0 -2 0 5

The diagonal is always symetric