matrix algebra

In mathematics, matrix algebra is about manipulating tables of numbers. Simple examples, you may have encounterd in school, are 2x2 matrices used to represent geometric transformations such as scaling, reflection or rotations. Matrices are used heavily in computation, especially for 2D or 3D geometry, for example the transform operator in CSS. In statistics and data anaysis, matrices often represent relationships between different kinds of things. For example where rows represent participants in an experiment and columns represent scores on different elements of the study.

Matrices can be added and subtracted, rather like numbers. For example, if we have a matrix representing each person's consumption of certain foods, we can take the matrices representing each week's consumption and add them together to get the year's consumption. Multiplication is also possible, returning to the participants vs. performance matrix, we might have another matrix representing how the different elements in the experiment contribute as a weighted sum towards a smaller number of summary measures; multiplying the participant–element-scores matrix by the element-scores–summary-measures matrix will give the matrix of summary scores for each participant.

Division is a bit more complicated as not all matrices have an inverse, but finding approximate inverses is a critical part of many statistical and data analysis methods.