Linear algebra matrix computations functions of matrices

Tutorial 7 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

mat = {{1., 2.}, {4., 5.}};
mat^0

Output

{{1., 1.}, {1., 1.}}

Step 2

MatrixExp[mat, 0]

Output

MatrixExp[{{1., 2.}, {4., 5.}}, 0]

Step 3

mat = {{1., 2.}, {5., 1.}};

No output - this step sets something up for the next one.

Step 4

MatrixPower[mat, 4]

Output

{{161., 88.}, {220., 161.}}

Step 5

matSq = mat.mat;matSq.matSq

Output

{{161., 88.}, {220., 161.}}

Step 6

MatrixExp[mat]

Output

{{32.16634241136035, 20.271009131525236}, {50.67752282881309, 32.16634241136035}}

Step 7

{eigs, vecs} = Eigensystem[mat];
vecs = Transpose[vecs];
vecsInv = Inverse[vecs];
vecs.DiagonalMatrix[Exp[eigs]].vecsInv

Output

{{32.16634241136035, 20.271009131525236}, {50.67752282881308, 32.16634241136034}}

Functions used