148 Section 12: Calculating with Matrices

operate on the matrices whose descriptors are placed in the X-register and (for some operations) the Y-register.

Two matrix operations – calculating a determinant and solving the matrix equation AX = B – involve calculating an LU decomposition (also known as an LU factorization) of the matrix specified in the X-register.*A matrix that is an LU decomposition is signified by two dashes following the matrix name in the display of its descriptor. (Refer to page 160 for using a matrix in LU form.)

The Result Matrix

For many operations discussed in this section, you need to define the matrix in which the result of the operation should be stored. This matrix is called the result matrix.

Other matrix operations do not use or affect the result matrix. (This is noted in the descriptions of these operations.) Such an operation either replaces the original matrix with the result of the operation (if the result is a matrix, such as a transpose) or returns a number to the X-register (if the result is a number, such as a row norm).

Before you perform an operation that uses the result matrix, you must designate the result matrix. Do this by pressing ´ < followed by the letter key specifying the matrix, (If the descriptor of the intended result matrix is already in the X-register, you can press O< instead.) The designated matrix remains the result matrix until another is designated.† To display the descriptor of the result matrix, press l<.

When you perform an operation that affects the result matrix, the matrix is automatically redimensioned to the proper size. If this redimensioning would require more additional elements than there are available in matrix memory (a maximum of 64 for all five matrices), then the operation can't be performed. This restriction can often be overcome by designating the result matrix to be one of the matrices being operated on. (However, there are certain operations for which the result matrix can not be the same one as either of the matrices being operated on – this is noted in the description of these operations.)

*The LU decomposition of a matrix A is another matrix in which is encoded a lower-triangular matrix, L, and an upper-triangular matrix, U, whose product LU equals matrix A (possibly with same rows interchanged). The HP-15C Advanced Functions Handbook discusses LU decomposition in detail.

† Matrix A is automatically designated as the result matrix whenever Continuous Memory is reset.