Block matrices are a great time-saver if one is tasked with multiplying two large matrices and one (or both) of them has an identity submatrix or, better still, a zero submatrix. However, in those cases when neither has any identity or zero submatrices, is there any advantage to dividing them into blocks before multiplying?
2026-04-06 10:54:52.1775472892
(New Kids on The) Block Matrix Multiplication
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Block matrix multiplication is very useful in a practical sense. For instance, the Strassen algorithm for matrix multiplication speeds up computation for large matrix products by exploiting block-matrix multiplication. Parallel and distributed algorithms for matrix multiplication also rely on block matrix multiplication in order to properly "distribute" the necessary computation.
It is also very useful for theoretical purposes. For instance, consider the inductive proof of the existence of the Schur decomposition of a matrix.