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Number Theory/Compute Inverse of a matrix having complex numbers.


Dear Prof Scott

Can we compute Inverse of a 3*3 matrix having all complex numbers?


Yes.  With any matrix, M, find upper and lower matrices L and U such that M = LU.
Upper and lower matrices are fairly easy to invert, so they can be inverted one at a time to find the inverse of the matrix.

Here is where you can find practically all operations known on matrices:

To invert a matrix, use

Now this only inverts real matrices, but the same operations performed on real numbers can also be applied to complex number such as addition and multiplication.  Subtraction is just the reverse of addition, and division is just the reverse of multiplication.  When complex numbers are used, multiplication by the conjugate is used to get a real denominator.

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Scott A Wilson


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