Which shows a very fast and simple way to get Eigen vectors for a 2x2 matrix. While harvard is quite respectable, I want to understand how this quick formula works and not take it on faith
Part 1 calculating the Eigen values is quite clear, they are using the characteristic polynomial to get the Eigen values.
Part 2, where they calculate the Eigen vectors is what I don't understand and have tried to prove but cannot.
I understand that that what matters with Eigen vectors is the ratio, not the value. For example, an Eigen value of 2, with vector 3, 4, I could have any other vector, example 6, 8, or 12, 16, etc... any scalar multiple.
In their example, given a matrix in the form a b c d, if b & c are zero, then the vectors are 1 0 and 0 1, which makes sense as you can scale these to any other size.
I don't understand the other two cases (when b=0, or c=0), or I presume the case when b & c are non-zero.
Can somebody offer an explanation or proof of this?