- #1

- 77

- 0

## Main Question or Discussion Point

Let A=

|1 2|

|0 3|

and B=

|1 0|

|0 3|

Show that A and B are not unitarily similar?

|1 2|

|0 3|

and B=

|1 0|

|0 3|

Show that A and B are not unitarily similar?

- Thread starter chuy52506
- Start date

- #1

- 77

- 0

Let A=

|1 2|

|0 3|

and B=

|1 0|

|0 3|

Show that A and B are not unitarily similar?

|1 2|

|0 3|

and B=

|1 0|

|0 3|

Show that A and B are not unitarily similar?

- #2

- 77

- 0

anyone have an idea of how to do this?

- #3

Deveno

Science Advisor

- 906

- 6

B* = (UAU*)* = (U*)*A*U* = UA*U*.

but B is symmetric so B = B*. hence we would have

UAU* = UA*U*, and so

U*UAU*U = U*UA*U*U and

A = A*, implying A is symmetric as well, which is false.

- #4

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- #5

Deveno

Science Advisor

- 906

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