a) Find Y such that is diagonal.

b) Find C such that

For a I get

I can't figure out b. Does it involve the Cayley-Hamilton theorem at all? I've only used that for solving not this way round. Thanks!

Printable View

- April 26th 2009, 05:17 AMThomas154321Matrix question

a) Find Y such that is diagonal.

b) Find C such that

For a I get

I can't figure out b. Does it involve the Cayley-Hamilton theorem at all? I've only used that for solving not this way round. Thanks! - April 26th 2009, 05:25 AMRapha
- April 26th 2009, 05:39 AMThomas154321
Thanks that's reassuring. (Happy)

I've also found another question I can't do:

Give an example of a square matrix over which is not similar to a diagonal matrix, and explain why this is the case.

No clue here. I know the two matrices are similar if they represent the same linear map with respect to two different bases, but other than that I don't know. - April 26th 2009, 06:10 AMZeroDivisor
Hi, regarding b):

we know that

And hence

Define

Then

Also,

so

is the matrix we are looking for.

If I work this out, I get

Best,

ZD - April 26th 2009, 06:10 AMmr fantastic