Patent of matrix multiplication algorithm

Matrix multiplication is an efficient algorithm, which can optimize some one-dimensional recursion to log( n) and find the path scheme, so it is a highly applied algorithm. Matrix is one of the basic concepts in linear algebra. The matrix of m×n is a digital array in which m×n numbers are arranged in m rows and n columns. Because it compactly concentrates a large amount of data, it can sometimes simply represent some complex models. Matrix multiplication looks strange, but it is actually very useful and widely used.

Chinese name: matrix multiplication

matrix multiplication

Basic attributes: combination, etc.

Category: symmetric matrix, etc.

Applied subject: mathematics

Application field: algebra

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Basic definition

Only when the number of columns of matrix A is equal to the number of rows of matrix B, A×B makes sense. Multiply an m×n matrix a(m, n) with an n×p matrix b(n, p) to get an m×p matrix c(m, p). Left multiplication: also called forward multiplication, that is, left multiplication (that is, before multiplication). For example, left times e is AE.

Matrix multiplication satisfies the associative law, but it does not satisfy the commutative law and the reduction law.

General moment multiplication can only be effective if it is combined with fast power. (Basically, all matrix multiplication uses fast powers. )

In a computer, a matrix is actually a two-dimensional array. A matrix of m rows and n columns can be multiplied by a matrix of n rows and p columns, and the result is a matrix of m rows and p columns, in which the number of the position of the I-th row and J-th column is the product of the number n of the I-th row of the first matrix multiplied by the number n of the J-th column of the second matrix. For example, the following formula indicates that a matrix with 2 rows and 2 columns is multiplied by a matrix with 2 rows and 3 columns, and the result is a matrix with 2 rows and 3 columns. Where 4 of the result matrix (the second (i) row and the second (j) column in the result matrix) =.

2 (second (i) row and first column of the first matrix) *2 (first row and second (j) column of the second matrix)

+

0 (row 2 (i), column 2 of the first matrix) * 1 (row 2 (j), column 2 of the second matrix):