Re: The cosine of a matrix

Am 24.10.2006 17:20 schrieb C6L1V@xxxxxxx:
schoenfeld.one@xxxxxxxxx wrote:
In this article we shall derive an explicit formula for the cosine of a
matrix.

All if this is old hat and well-known; see, eg., Gantmacher, or
Lancaster.

I have a related question, though: is it true that for a matrix A we
have
(sin(A))^2 + (cos(A))^2 = I? (I = identity matrix)

I think, this is simple:
it sums the (diagonal matrix of) eigenvalues to 1 and leads
by
E *cos(D)²*E^-1 + E *sin(D)²*E^-1

(where E are the eigenmatrices and D are the
diagonalmatrices of eigenvalues) to

E*I*E^-1 = I

Gottfried Helms
.