Space of all matrices with given column space
Let $V$ be the vector space of all $m \times n$ (assume $m \leq n$) matrices $M$ over a field $\mathbb{F}$ whose column space satisfies $\operatorname{colsp}(M) \subseteq W$, where $W \subseteq \mathbb{F}^m$ is a given subspace. Prove that $\operatorname{dim}_\mathbb{F}(V) = n \operatorname{dim}_\mathbb{F}(W)$.
Ribs
72
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Martin
1.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 443 views
- $10.00
Related Questions
- Linear Algebra - Matrices and Inverses Matrices
- Show that $tr(\sqrt{\sqrt A B \sqrt A})\leq 1$ , where both $A$ and $B$ are positive semidefinite with $tr(A)=tr(B)=1.$
- For what values k is the system consistent?
- Consider the plane in R^4 , calculate an orthonormal basis
- Linear Algebra - matrices and vectors
- linear algebra
- Linear Algebra Assistance: Linear Combinations of Vectors
- Linear Algebra Exam
