Accessing eigenvalue results

The following operators and operands are used to access the results of the INVERT:  and EIGEN:  commands. Suppose that the matrix (A must be symmetric) is supplied to either of these two commands, and suppose that the ordered eigenvalues of are corresponding to eigenvectors . These eigenvectors are optionally retained as assignments using the eig  argument to the KEEP:  command, and might be accessed using the ascf  operator.

Matrix rank

 

Usage

• eigrank  operand.

This returns the number of positive eigenvalues of the matrix A. If the matrix was non-negative definite then this is equivalent to the rank.  

Matrix trace

 

Usage

• eigtr  operand.

This returns the trace of the matrix A.  

Matrix eigenvalues

 

Usage

• eig  operator; one argument i in parenthesis. i is any valid equation, rounded to the nearest integer.

This returns the ith ordered eigenvalue of the matrix A, namely , provided that . Otherwise an error occurs.