Matrix Multiplication:: Coresponds to Geometric operations of scaling and rotating
Matrix Translation:: it is possible to do with matrix multiplication, you just need a higher dimension, using with M×A M=[1,0,t_x,0,1,t_y,0,0,1] and A=[x,y,1] then only take the first two components of A. Look up ‘Homogenous Coordinates’ to find more info on this method, it is commonly used in computer games.
Matrix Eigenvectors Eigenvalues:: An eigenvector is a vector whose ‘direction’ is unaltered by a linear transformation \([M]\), applying \([M]\) merely scales the eigenvector by ‘λ’ ammount (λ is the eigenvalue, note λ can be negative which would be a 180° change), so Mv=λv
Matrix Characteristic Equation:: \(\det([M]-λI) = 0\) subtract the various eigenvalues from the diagonals