How to use MATLAB to complete the rank of a matrix?

Question

Ali Almakhmari 2023-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/2045615-how-to-use-matlab-to-complete-the-rank-of-a-matrix

编辑： John D'Errico 2023-11-10

I have this matrix here:

Wc=[0	0.285714285714286	0	0.918367346938775	0	9.83965014577259
0.285714285714286	0	0.918367346938775	0	9.83965014577259	0
0	-0.214285714285714	0	-2.29591836734694	0	-24.5991253644315
-0.214285714285714	0	-2.29591836734694	0	-24.5991253644315	0
0	-0.214285714285714	0	-2.29591836734694	0	-24.5991253644315
-0.214285714285714	0	-2.29591836734694	0	-24.5991253644315	0];

The rank of this matrix is 4 because column 3 and column 4 are linearly dependent. How can I use MATLAB to replace column 3 and column 4 with columns that will make the rank full (six)?

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Answer 1

John D'Errico 2023-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/2045615-how-to-use-matlab-to-complete-the-rank-of-a-matrix#answer_1350585

编辑：John D'Errico 2023-11-10

Trivial.

Replace the offending columns with vectors of random numbers. DONE. With probability 1, the result will be full rank. NOT random integers. Use rand, or randn.