Examples of using transposed matrices

　・In Japanese
＜premise knowledge＞
　・Matrix multiplication

■What is a transposed matrix?

A transposed matrix is a matrix whose rows and columns are interchanged. Represented as A^T.

■Properties of transposed matrices

The following holds: However, X and Y are limited to sizes that can be multiplied.






tr is called a trace and is the diagonal sum of the matrix.

And if the matrix is symmetric, then:

■Examples of using transposed matrices

As below. The product of the matrix and the transposed matrix is the sum of squares.



At this time, if x_i is some error from the reference, it will be the residual sum of squares, which is useful for calculating the least squares method. In addition, the following formula weights each term, which is useful for designing the optimum regulator for modern control.

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