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Computing the inverse of a matrix

There are some situations when computing the inverse of a matrix is needed. Based on the fact that

where is the identity matrix, the inverse of , , satisfies the equation

If we write explicitly the column composition of and the identity matrix we have

From here we see that, columnwise, the above relation is equivalent to solving 3 systems with the same matrix A:

For our example we get

Adrian Sandu 2001-08-26