# Updating the inverse of a matrix

Using the Sherman-Morrison formula, update R (the inverse of Q). The Sherman-Morrison formula also updates the determinant of the matrix. If i = n, stop * * NOTES: * * This algorithm has the advantage of calculating the determinant of the original * matrix in the process.

Thanks to rank-one updates, we can bring that cost down to .

You can also find the inverse using an advanced graphing calculator.

/* I took this from my implementation of CMatrix * It works, but I'm not sure if it's the most efficient algorithm. Start with Q = Identity, whose inverse is R = Identity.

For example, if a problem requires you to divide by a fraction, you can more easily multiply by its reciprocal. Similarly, since there is no division operator for matrices, you need to multiply by the inverse matrix.

Calculating the inverse of a 3x3 matrix by hand is a tedious job, but worth reviewing.

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A procedure for implementing this algorithm in existing computer code is presented.

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