Linear Algebra

[RicherThanRichie]

Suppose U is an nxn orthogonal, sysmetric (U^T=U) matrix
a) show that the only eigenvalues U has are +1 and -1


any help would be apprciated

[RoundTower]

If you bought the textbook recommended for your course you will find this, or something that points to it, somewhere.

[shortline99]

I wouldn't be surprised if the answer to this question was in the table of contents for that textbook.

[Mik1w]

if its orthonormal matrix n^2, its proven that ||Qx||=||x|| for every vector x in real^n, from this you can see that if you find an eigenvalue y of the orthonormal matrix, it must be that a corresponding eigenvector v is in real^n and therefore ||Qv||= y||v|| = ||v|| => |y|=1. this is true for complex eigenvalues too.

[RicherThanRichie]

Thanks for the help, the question was asked by a friend and I do not take linear algebra. Otherwise I agree, looking in a textbook would be helpful. Thanks for the answer Mik.

[Mik1w]

no problem. my exam for this still is tomorrow.

[KingNeo]

I took Linear Algebra twice and it sucked both times. Once as an elective....don't ask.

Looking over this post this stuff looks like a foreign language to me now.