HP 15c - Manual (Page 160)

160 Section 12: Calculating with Matrices
Using Matrices in LU Form
As noted earlier, two matrix operations (calculating a determinant and
solving the matrix equation (AX = B) create an LU decomposition of the
matrix specified in the X-register. The descriptor of such a matrix has two
dashes following the matrix name. A matrix in LU form has elements that
differ from the elements of the original matrix.
However, the descriptor for a matrix in LU form can be used in place of the
descriptor for the original matrix for operations involving the inverse of the
matrix and for the determinant operation. That is, either the original matrix
or its LU decomposition can be used for these operations:
∕
÷ for the matrix in the X-register
> 9
For these three functions, using the LU form of the matrix to be inverted
gives a result that is identical to that using the original matrix.
As an example, if you solved the matrix equation AX = B, matrix A would
be changed to its LU form. If you wanted to change the B matrix and solve
the equation again, you could do so without changing the A matrix – the LU
matrix will give the correct solution.
For all other matrix operations, a matrix that is an LU decomposition is not
recognized as representing its original matrix. Instead, the elements of the
LU matrix are used just as they appear in matrix memory and the result is
not the result you would obtain using the original matrix.
Calculations With Complex Matrices
The HP-15C enables you to perform matrix multiplication and matrix
inversion with complex matrices (that is, matrices whose elements are
complex numbers) and to solve systems of complex equations (that is,
equations whose coefficients and variables are complex).
However, the HP-15C stores and operates on only real matrices. The
capability of doing calculations with complex matrices is completely
independent of the capability of doing calculations with complex numbers
described in the preceding section. You don’t need to activate Complex
mode for calculations with complex matrices.