given X = [[1,0],[0,0]] and Y = [[0,0],[0,1]], aXY = 0 for all a (because XY == [[0,0],[0,0]]).
But, given V = [[1,1],[1,1]] (or, in fact, a lot of other matrices/linear transforms), XVT = [[0,1],[0,0]], which blocks all vertical components and rotates the horizontal component 90 degrees. So if you imagine light as a wave with a horizontal and vertical component, and the polarizing filter applies a linear transform to the light.
given X = [[1,0],[0,0]] and Y = [[0,0],[0,1]], aXY = 0 for all a (because XY == [[0,0],[0,0]]).
But, given V = [[1,1],[1,1]] (or, in fact, a lot of other matrices/linear transforms), XVT = [[0,1],[0,0]], which blocks all vertical components and rotates the horizontal component 90 degrees. So if you imagine light as a wave with a horizontal and vertical component, and the polarizing filter applies a linear transform to the light.