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...Lecture notes matrix algebra part d similar matrices and diagonalization peter j hammond minor revision september th university of warwick eca maths for economists outline eigenvalues eigenvectors real case the complex linear independence diagonalizing a general properties adjoint symmetric aself has only orthogonal projections rayleigh quotient spectral theorem quadratic forms their deniteness eigenvalue test sylvester s criterion denitions in denition consider any n scalar r is an just equation ax x non zero solution this rn eigenvector pair eigenpair spectrum set sa its let sr denote subset sc c which satises summary main wewill be demonstrating following number even members are conjugate pairs i possible but not if odd one...