Characteristic equation and eigenvalues for matrix order 2,3,4,5 on the HP41
EIGEN computes the characteristic equation and eigenvalues of matrices of order 2, 3, 4, and 5. It computes the coefficients
of the characteristic polynomial directly, then solves for the roots of the polynomial. Routines from the MATHSTAT (or MATH I)
module are used—EIGEN expects that MATRIX is run first to enter the matrix elements, then both DET (XROM 01,06) and ROOTS
(XROM 01,12) are called.
Compared to alternate approaches such as Samuelson's formula (see, e.g.,
Jean-Marc Baillard's program CP), computing the polynomial coefficients
directly for low-order matrices has the advantage of speed at the cost of longer code, at least for order 5 matrices, and
limited matrix order. Note that the method used by EIGEN is in general the opposite approach of an algorithm that obtains
the best numerical accuracy (where the eigenvalues are computed first, then the polynomial coefficients; see Matlab's POLY
function). However, the accuracy issues associated with computing polynomial coefficients and the
ill-conditioning of computing polynomial roots are not a concern for very low order matrices—compare Matlab's
ROOTS(POLY(1:5)) and ROOTS(POLY(1:21)). (And computations for higher order matrices are best done on a computer, if only for
data entry!)
To load EIGEN, first install the MATHSTAT (or MATH I) module and XEQ SIZE 090 to allocate sufficient program and memory
registers. To run EIGEN, XEQ MATRIX (MATHSTAT/MATH I module) and enter the matrix elements as prompted. Then XEQ EIGEN. The
coefficients of the characteristic polynomial will first be displayed, then their roots, the eigenvalues. R/S through each of
the displays.
This program is generated by Antonio Lagana's i41CX+ iPhone emulator.