Show that if A is an nxn matrix then

I'm not good with adjoints...first thing that comes to mind is

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- February 9th 2011, 11:59 AMJskidtheoretical question involving determinant and adjoint
Show that if A is an nxn matrix then

I'm not good with adjoints...first thing that comes to mind is - February 9th 2011, 04:16 PMDrexel28
- February 9th 2011, 07:40 PMJskid
- February 9th 2011, 07:46 PMDrexel28
What you are calling the adjoint is what I call the adjugate. The adjoint of an endomorphism (if it exists) on an inner product space is the unique endomorphism such that for every . It has the property that if you fix an orthonormal ordered basis (assuming ) then (where here is the matrix representation with respect to that ordered basis, and ).

- February 9th 2011, 08:17 PMdwsmith
- April 9th 2013, 07:05 PMmathguy25Re: theoretical question involving determinant and adjoint
My linear book describes adjoint as the linear operator T* such that (T*(v), w) = (v, T(w)). * relates to linear operators in much the same way as * relates to matrices.

Of course, this isn't the first time mathematicians use the same word to describe multiple mathematical concepts. - April 10th 2013, 06:31 AMtopsquarkRe: theoretical question involving determinant and adjoint