MATH 305 Lecture 9: Review: Partitions of a Matrix
26 Apr 2016
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Example 1: given matrices a and b, week 5, mon 4/25/2016. Definition: if partition a matrix by a number of blocks, we call this matrix as a partitioned matrix (block matrix) Rules for multiply two partitioned matrices are the same as regular matrix multiplication. To use the formula for block matrix multiplication ab, the row partition of b has to be the same as the column partition of a. Suppose a is a m n matrix, let a1, a2,,an be the n columns of a, then we can write. Let (ab)j denote the jth column of matrix ab. Example 4: let a and b be two n n square matrices whose last column are the vector en. Prove that the last column for ab is still en. Let (ab)it denote the ith row of matrix ab (a) let ait be the ith row of matrix a. Write a1t (b) write the first row of ab.
