“block multiplication”的概念、定义、翻译、参考文献-科学参考

block multiplication

Mathematics

单词	block multiplication
释义	block multiplication Mathematics Multiplication of matrices where the entries are submatrices rather than single elements; the submatrices still multiply as if they were entries. For example, given two 3×3 matrices of the form $A_{1} = (\begin{matrix} M_{1} & v_{1} \\ w_{1} & c_{1} \end{matrix}) a n d A_{2} = (\begin{matrix} M_{2} & v_{2} \\ w_{2} & c_{2} \end{matrix})$ where the M_i, v_i, w_i, c_i are respectively 2 × 2, 2 × 1, 1 × 2, 1 × 1 matrices, then their product equals $A_{1} A_{2} = (\begin{matrix} M_{1} M_{2} + v_{1} w_{2} & M_{1} v_{2} + v_{1} c_{2} \\ w_{1} M_{2} + c_{1} w_{2} & c_{1} c_{2} \end{matrix}) .$
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