Transposing Matrices

• May 14th 2011, 06:45 PM
rorosingsong
Transposing Matrices
Hi, i'm struggling with this question and really need a push in the right direction... i haven't the faintest idea of what to do here... we haven't learnt about transposing maxtrices yet, I just saw something about it in a text book so I have a vague idea, but I don't really know how to go about proving this:

If A is an m x n matrix with (i,j)- entry $a_{ij}$, let $A^{\dagger}$ be the n x m matrix with (i,j)- entry $a_{ji}$. Show that if the product C= AB is defined, then so is $B^{\dagger}A^{\dagger}$, and that $B^{\dagger}A^{\dagger} = C^{\dagger}$.

rorosingsong
• May 14th 2011, 06:55 PM
pickslides
I think you need to apply the properties of matrix tranposition

If C = AB then C' = (AB)' = A'B'

More here

Transpose - Wikipedia, the free encyclopedia
• May 15th 2011, 01:36 AM
rorosingsong
Thanks pickslides! Appreciate it. =)
• May 15th 2011, 02:07 AM
Prove It
Quote:

Originally Posted by pickslides
I think you need to apply the properties of matrix tranposition

If C = AB then C' = (AB)' = A'B'

More here

Transpose - Wikipedia, the free encyclopedia

Except that $\displaystyle (\mathbf{AB})^T \neq \mathbf{A}^T\mathbf{B}^T$.

However, $\displaystyle (\mathbf{AB})^T = \mathbf{B}^T\mathbf{A}^T$.