Linear independent matrices

linear-algebra

asked 2022-08-02 00:53:50 +0100

bobby.mir
65 ●1 ●1 ●6

updated 2022-08-02 21:05:35 +0100

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?

edit retag flag offensive close merge delete

add a comment

1 Answer

Sort by » oldest newest most voted

answered 2022-08-02 05:42:14 +0100

Max Alekseyev

6488 ●9 ●47 ●153

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())])

edit flag offensive delete link

Comments

I was wondering if there is a method for avoiding flatting.

bobby.mir ( 2022-08-02 20:08:05 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2022-08-02 00:53:50 +0100

Seen: 970 times

Last updated: Aug 02 '22

Linear independent matrices edit