describe all normal nxn matrices hat have only one eigenvalue.

This is over the complex.

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- May 21st 2008, 11:52 AMmathisthebestpuzzledescribe all normal matrixs
describe all normal nxn matrices hat have only one eigenvalue.

This is over the complex. - May 22nd 2008, 06:12 AMCaptainBlack
- May 22nd 2008, 07:09 AMmathisthebestpuzzle
i'm sorry captain black but i do not understand your response at all.

- May 22nd 2008, 10:47 AMMoo
- May 22nd 2008, 11:50 AMCaptainBlack
- May 22nd 2008, 04:17 PMmathisthebestpuzzle
A normal matrix is one such that AA*=A*A where A* denotes the conjugate transpose.

When you diagonalize a normal matrix A, the diagonal matrix contains the eigenvalues for the map.

Since these matrices are restricted to having only one eigenvalue then:

All normal nxn matrices over the Complex space are similar to a diagonal matrix that has the single eigenvalue for every entry in the diagonal.

Is this correct? Is there more that can be said? Captain. THANK YOU - May 22nd 2008, 04:57 PMmathisthebestpuzzle
- May 22nd 2008, 07:43 PMCaptainBlack
- May 22nd 2008, 10:26 PMmathisthebestpuzzle
what is the notation ?

- May 22nd 2008, 10:44 PMCaptainBlack