Vector subspace as the space of solutions to matrix multiplication

uman · Feb 6, 2009

Given a subset W of a vector space V = F^n (for some field F), prove that W is the subspace of solutions of the matrix equation AX = 0 for some A.

HallsofIvy · Feb 6, 2009

Why?

Seriously, this sounds like a homework problem so it should be in the homework section.

In any case, define the orthogonal complement of W and let A be the projection onto that complement.

Hurkyl · Feb 6, 2009

I would just solve for A myself.

Vector subspace as the space of solutions to matrix multiplication

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