Convolution

$Convolution of two square pulses: the resulting waveform is a triangular pulse. One of the functions (in this case g) is first reflected about \ au=0 and then offset by t, making it g(t-\ au). The area under the resulting product gives the convolution at t. The horizontal axis is \ au for f and g, and t for f\ast g.$

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

More at Wikipedia

Toeplitz matrix (convolutions can be considered a Toeplitz matrix operation where each row is a shifted copy of the convolution kernel)

Circulant matrix