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

Question

Ohad Shapira 2021-1-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/712148-find-the-symmetric-and-skew-symmetric-matrices-by-2x2-blocks

评论： Matt J 2021-1-10

在 MATLAB Online 中打开

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;
    ]

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Matt J 2021-1-10

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

0,3,

4,0,

is not symmetric.

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Answer 1

Matt J 2021-1-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/712148-find-the-symmetric-and-skew-symmetric-matrices-by-2x2-blocks#answer_593978

编辑：Matt J 2021-1-8

在 MATLAB Online 中打开

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
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