Linear Algebra Done Right · Problem 9C.5

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · determinants

Problem

Suppose AA is a block upper-triangular matrix A=(A1∗⋱0Am),A = \begin{pmatrix} A_1 & & * \\ & \ddots & \\ 0 & & A_m \end{pmatrix}, where each AkA_k along the diagonal is a square matrix. Prove that det⁡A=(det⁡A1)⋯(det⁡Am).\det A = (\det A_1) \cdots (\det A_m).

Related theory

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