Question

If you're given the span of a matrix, A, how would you determine the basis for an matrix orthogonal to A (i.e. A perpendicular)

Answer 1

is it gram schmidt?

Answer 2

gram schmidt would give you an orthogonal basis for the span. Im not sure if thats what your question is asking for.

Answer 3

How im reading it is you want a new space, that is orthogonal to the span ( or Column Space) of a given matrix.

Answer 4

yes

Answer 5

So what i think you should do is get those basis vectors, and make them rows of a new matrix. If A was the original matrix, this new matrix would be the transpose of A. Then what you want is the Null Space of A transpose.

Answer 6

You want all the vectors that satisfy:
\[A^Tx = 0\]

Answer 7

oic...that really is quite simple then, lol. thanks a bunch!

Answer 8

this is the reasoning behind that argument.
Just for further clarification.