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Linear algebra

In matrix algebra, square or rectangular blocks of numbers are manipulated as though they were numbers themselves: matrices can be added and multiplied, and in some cases, a version of division also exists. Dividing by a matrix means, more precisely, multiplying by its inverse. Not all matrices have inverses. For example, a matrix containing only zeros is not invertible.

One can define a pseudo-division, by setting a / b = ab, in which b represents the pseudoinverse of b. It can be proven that if b exists, then b = b. If b equals 0, then b = 0.