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Matrix / Matrix multiplication / Matrix fast recursive power optimization
The popular version of content (technical definition ah terms of what I would not)
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matrix
Matrix (Matrix) is a bunch of numbers to fill in the rectangular -shaped table (so called matrix?), Like:
This is a matrix of m rows and n columns, which referred to the number n × m matrix A element, referred to as the element, the number of aij of the matrix A i-th row j-th column, called a matrix A of (i, j) element , as the number of aij (i, j) elements may be referred to as a matrix (aij) or (aij) m × n, m × n matrix a is also referred to as Amn .
Then passing mention a nozzle matrix addition and subtraction, addition and subtraction on the corresponding element on the bin ...
Matrix Multiplication
All matrix multiplication operation in line with the law of real multiplications addition commutativity reason can be seen from the calculation method
For convenience, I will distinguish two factor matrices so: called called left right left right of the matrix matrix
as a result of the matrix C in (i, j) element is the i-th row j-th column matrix of left and right matrix corresponding to elements are multiplied and (more convoluted: and the product of the corresponding elements)
Example: results of the matrix (1,1) = 1 element * 2 * 7 + 9 + 11 = 58 * 3
DETAILED each element as follows:
Easy to see that when only the number of columns equal to the number of rows left and right matrix matrix equation is meaningful
so the matrix multiplication requires three matrix of the form:
A XY * B YZ = C an xz
The results depend on the ranks of the matrix factor matrix
Recursive matrix multiplication optimization
finally come
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