Orthogonal matrices (1 Viewer)

[acmilan]

Is it always true that a 3x3 orthogonal matrix with determinant 1 has an eigenvalue 1? Because the notes say so, but I have a matrix which is orthogonal and has determinant 1, but according to maple it has 2 imaginary eigenvalues and one 0. Am I doing something wrong?

 

[acmilan]

Never mind, was entering the wrong matrix in it seems :/

 

[me121]

I know what a matrix is, and i know what an orthogonal drawing is, but what is an orthogonal matrix?

 

[Affinity]

hmm

definition one: the matrix M has the property that M*transpose(M) = Identity matrix.
by extension, a matrix whose inverse is it's transpose


definition two: A square matrix with orthonormal columns.

definition three: A matrix representing an Isometric map from R^n into itself
that is |Ax| = |x| for all x.

definition 3 is perhaps the best, coz it can be generalised to other inner product spaces.