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asked 2 years ago

bobby.mir gravatar image

Linear independent matrices

When you have a standard vector space like Q3 with some vectors, we can check whether they are linearly independent or not.

v1 = vector(QQ, [0,1,-3])
v2 = vector(QQ, [4,1,0])
V = QQ^3
relations = V.linear_dependence([v1, v2]); relations

Now my question is the following is there a direct method to check whether a couple of matrices are linearly independent in the set of n×n matrices over R?

Linear independent matrices

When you have a standard vector space like Q3 with some vectors, we can check whether they are linearly independent or not.

v1 = vector(QQ, [0,1,-3])
v2 = vector(QQ, [4,1,0])
V = QQ^3
relations = V.linear_dependence([v1, v2]); relations

Now my question is the following is there a direct method to check whether a couple of matrices are linearly independent in the set of n×n matrices over $\mathbb R$?R$? More precisely how can I convert

MatrixSpace(CDF,4,4)

to a vector space and get vectors like above?