Using the operations of multiplication by a scalar and sum of matrices, it is possible to create an image transition effect commonly used, for instance, in Power Point presentations and slide shows. More precisely, consider two grayscale images of the same size, represented by the matrices A and B. For each scalar (real number) t in the interval [0, 1], define the matrix

M(t) = (1 − t) A + t B.

Notice that M(0) = A, M(1) = B and, for each t between 0 and 1, the elements of the matrix M(t) are between the elements of the matrices A and Z. Therefore, when t varies from 0 to 1, the matrix M(t) varies from A to Z. For the case of color images, the transformation above must be applied to the matrices R, G and B that compose each image. The applet below illustrates this idea: move the slider to adjust the value of t and visualize the corresponding image. To select different images, click on the icons at the bottom of this page.