The bookUnit 1 · Determinants and Matrix Tricks29 / 83

Determinants, trace, block matrices, rank inequalities

Why this is asked: Block formulas and the trace/determinant identities turn hard computations into one-liners. det(I + AB) = det(I + BA) is the single most useful trick here.

Determinants, trace and block matrices

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Block matrices: which determinant formulas are actually trueinteractive

The triangular block rule, and the tempting formula that fails unless the blocks commute.

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Let A = J − I where J is the 5×5 all-ones matrix. Then det A equals

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