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...Determinants september one of the rst things that most students learn about in linear algebra is determinant a matrix lots useful formulas for and matrices can be expressed terms played central role years ago when were tiny nowadays are much less as practical tool although they still occasionally show up related also proving theorems basic computational problem however don t scale big there almost always better way computing something than using explicit cofactors cramer s rule other tricks small it important to know what their properties we mainly use conceptual help us understand eigenvalues via characteristic polynomial again this not which computed by very dierent methods expectation singular zero theproperty given square det some number if only example following its julia nonzero out you may even remember formula but second column twice so many authors including strang book abbreviated notation deta i won here because think enough anymore deserve own punctuation anyway looks too l...