Matrix multiplication

・In Japanese
[premise knowledge]
・Dot product

■How to Multiply matrices

The basic rule is that there are combinations that can be multiplied, and the number of columns in the left term must match the number of rows in the right term. Also, the number of matrices after multiplication is the same as the number of rows in the left term and the number of columns in the right term.



Also, even if the order to multiply the matrix is reversed, the answer will not be the same as before the reverse.

■Difference from Dot product and Hadamard product

A dot product (also called an inner product) is obtained as follows. A dot symbol is required between vectors, otherwise it is treated as Matrix multiplication, but in this case 1x2 and 1x2 cannot be multiplied.



Also, the following calculation is called Hadamard product, which is also different from Matrix multiplication.

■ Matrix multiplication formula

Define A,B,C,D as follows


Indicates the main calculation method.

■Concrete example of Matrix multiplication

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