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...Short guides to microeconometrics kurt schmidheiny klaus neusser fall university of basel elements matrix algebra contents denitions operations rank a special functions square matrices systems equations eigenvalue vector and decomposition quadratic forms partitioned derivatives with kronecker product references formula sources proofs version foreword these lecture notes are supposed summarize the main results concern ing as they used in econometrics economics for deeper discussion material interested reader should consult listed at end is rectangular array numbers here we consider only real if has n rows m columns say that dimension denote by capital bold letters ij nm called an column similarly row vectors b scalar which denoted italic letter null o whose all equal zero i e j same number symmetric such ji diagonal ele ments identity one or said be upper triangular whenever lower two linearly dependent there exist scalars both not otherwise independent equality have their respective tr...