A = [ b c ... 0000000000000000000 ]
[ c b c ... .000000000000000 0]
[ ... ]
[ 000000000000000000 c b c ]
[ 000000000000000000 b c ]
where a,b are real. This matrix is tridigonal and symmetric.
I need to show that this matrix has e-values lamda_i = b +2cos((i * pi)/(N+1))
and e-vectors x_i = [sin ((i* pi)/(N+1), sin ((2*i*pi)/(N+1)), ...., sin((N*i*pi)/(N+1))]
The Attempt at a Solution
I could find the deterministic equation to find the e-values but i don't see how that gives rise to trigonometric functions.