Symbolic Analysis of Dominant Eigenvalue

> t := 't':

> A[2,1] := t:

> evalm( A );

>

> eigenvalues( A );

Error, (in linalg/evalf) matrix entries must all evaluate to float

>

Even though Maple does not want to compute the eigenvalues of this matrix, we can use the fact that eigenvalues are roots of the characteristic polynomial to overcome this obstacle. The characteristic polynomial is

> p := charpoly( A, lambda );

The roots of this cubic polynomial are (exactly):

> solve( p=0, lambda );

>

Of the three roots, only the first is real valued:

> lambda1 := %[1];

> plot( [lambda1, 1], t=0 .. 0.5, title="Dominant eigenvalues as a function of t" );

>

The value of t for which the dominant eigenvalue is 1 is

> solve( lambda1=1., t );

>