MATLAB POLYSPACE RELEASE NOTES Manuel d'utilisateur télécharger pdf (Page 45)

More About Matrices and Arrays

0.1471 0.2941 0.3235 0.2353

0.2647 0.1765 0.2059 0.3529

0.1176 0.4412 0.4118 0.0294

Such matric es represent the tr ansition probabilities in a Markov process.

Repeated powers of the matrix represent repeated steps of the process. For

our example, the fifth power

P^5

0.2507 0.2495 0.2494 0.2504

0.2497 0.2501 0.2502 0.2500

0.2500 0.2498 0.2499 0.2503

0.2496 0.2506 0.2505 0.2493

This shows that as approaches infinity, all the elements in the th power,

, approach .

Finally, the c oefficients in the characteristic polynomial

poly(A)

are

1 -34 -64 2176 0

This indicates that the characteristic polynomial

The constant term is zero, because the matrix is singular, and the coefficient

of the cubic term is -34, because the matrix is magic!

2-23

1 2 ... 40 41 42 43 44 45 46 47 48 49 50 ... 239 240

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MATLAB POLYSPACE RELEASE NOTES Manuel d'utilisateur Page 45