Eigenvectors

[DrD]

Commands exist to return eigenvectors for a given matrix; but difficulties arise with these, because of the nature of exact, (versus approximate), entries within a matrix.
exact(matrix) can be helpful here, but this layers confusion, delaying productivity, and becoming a frustrating part of the prime CAS.

For example, (Markov) matrix:

[CAS]
a:=[[0.9,0.2], [0.1,0.8]]; Entries with approximate values
a1:=[[9/10,2/10], [1/10,8/10]]; The same matrix with exact values

eigenvects(a); ==> [[0.894427191,−0.7453559925],[0.4472135955,0.7453559925]];

// Using either of these:
eigenvects(exact(a));
eigenvects(a1); // ==> [[2,-1],[1,1]]; MUCH nicer to work with

Wolfram Alpha returns [[2,-1],[1,1]], in BOTH cases, visibly easier to work with, and quickly compares to the result obtained, by hand, when manually deriving the eigenvectors.

Comments?

-Dale-