Linear independent matrices

Loading [MathJax]/jax/output/HTML-CSS/jax.js

First time here? Check out the FAQ!

linear-algebra

bobby.mir
65 ●1 ●1 ●6

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?

add a comment

1 Answer

Sort by » oldest newest most voted

answered 2 years ago

Max Alekseyev

6932 ●9 ●52 ●162

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())])

link

Comments

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

bobby.mir ( 2 years ago )

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: 2 years ago

Seen: 1,123 times

Last updated: Aug 02 '22

Linear independent matrices savecancel

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions