Let A be a diagonal matrix.

Prove that A is unitary iff its diagonal entries are complex unit numbers.

Unitary is

Let

Now what can I do?

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- Nov 4th 2011, 01:52 PMdwsmithA is unitary iff the diagonals are complex unit numbers
Let A be a diagonal matrix.

Prove that A is unitary iff its diagonal entries are complex unit numbers.

Unitary is

Let

Now what can I do? - Nov 4th 2011, 02:00 PMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
Well, if you take

what does that tell you? - Nov 4th 2011, 02:01 PMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 4th 2011, 02:05 PMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
The LHS is what you get from taking the component of the product What do you know about the RHS?

- Nov 4th 2011, 02:07 PMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 4th 2011, 02:10 PMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
- Nov 4th 2011, 02:12 PMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 4th 2011, 02:36 PMDevenoRe: A is unitary iff the diagonals are complex unit numbers
if , what are the diagonal elements of the two matrices on the left, and the matrix on the right?

the equality sign says they are the same matrices, and matrix equality means every entry is equal. - Nov 5th 2011, 09:09 AMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 5th 2011, 09:12 AMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
- Nov 5th 2011, 09:23 AMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 5th 2011, 11:00 AMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
So far as I know, the definition of a matrix inverse that is typically used is the one I gave in Post # 6. The inverse of 5 is that number such that, when you multiply it by 5, you get 1. So that'd be 1/5, because 5(1/5)=(1/5)5=1. Similarly, the inverse of

is

because

I'm not sure I understand your definition of the matrix inverse. What does the asterisk mean in your definition? - Nov 5th 2011, 11:37 AMdwsmithRe: A is unitary iff the diagonals are complex unit numbers
- Nov 5th 2011, 11:54 AMAckbeetRe: A is unitary iff the diagonals are complex unit numbers
Well, ok, but is not the inverse of If you look here, you will see the formula where is the cofactor matrix.