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Linear independent matrices

asked 2022-08-02 00:53:50 +0200

bobby.mir gravatar image

updated 2022-08-02 21:05:35 +0200

When you have a standard vector space like $\mathbb Q^3$ 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\times n $ matrices over $\mathbb R$? More precisely how can I convert

MatrixSpace(CDF,4,4)

to a vector space and get vectors like above?

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answered 2022-08-02 05:42:14 +0200

Max Alekseyev gravatar image

You can flatten the matrices and use the same .linear_dependence method:

m1 = Matrix(QQ, [[0,1],[2,3]])
m2 = Matrix(QQ, [[0,2],[4,6]])
V = QQ^4
V.linear_dependence([vector(m1.list()), vector(m2.list())])
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I was wondering if there is a method for avoiding flatting.

bobby.mir gravatar imagebobby.mir ( 2022-08-02 20:08:05 +0200 )edit

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Asked: 2022-08-02 00:53:50 +0200

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Last updated: Aug 02