ok so there's these things called Linear Transformations & so basically what happens is you have this underlying matrix & the column vectors of the matrix represent the image of the basis vectors under the transformation
also so sometimes you can conjugate them and replace all the i's w -i's and sometimes you also transpose them which means you mirror them around the main diagonal and also the main diagonal of diagonalized matrix is the eigenvalues & if you add the main diagonal of a triangular matrix you get the determinant so that's kinda cool I guess

eigenvectors are the ones that are only scaled under tranformation, eigenvalues are the scalar multiples of the eigenvectors

ok this is me Ashley Vu officially me for real and that is all kids thanks for reading !