Capital letters, like, indicate matrices.
Transposing a matrix, of elements , is the operation which switches the row and column positions of each element:
Transpose of the transpose:
Transpose of the sum:
Transpose of the product:
The first one follows straightly from definition.
The second one is straightforward just because the elements ofare the sums of elements inand.
The third one is easily proven using the fact that , so that we can say and , so the two things are the same.
Given two matrices A and B (typically kernel and image, as this is used in computer vision),
their convolution is obtained via the multiplication of locationally similar entries and summing:
This procedure is loosely related to mathematical convolution.
Given matrix M, its Frobenious norm is the square root of the sum of the squares of its elements.