Linear Algebra 16b: Algebraic Derivation of the Eigenvalue Algorithm

[RitterTree]

Thank you sir, your exposure is so linear and clean that understanding is effortless.

[tangolasher]

Very confused - so you're saying that you can ONLY find eigen values for a singular matrix (ie, a matrix that has a NULL SPACE)? because you try to find the vector that will bring the value of a matrix to 0, right? But how about a reflection matrix, which is NON-SINGULAR? Doesn't that matrix still have eigen values? (the vector perpendicular to the axis of reflection, which gives an eigen value of -1). It has eigen values, but it doesn't collapse space down to a lower dimension like a projection matrix, and therefore it is NON-SINGULAR, right? So this formula wouldn't work for a reflection matrix because it never takes a vector to 0? Very confused!