MATLAB POLYSPACE RELEASE NOTES User Manual download pdf (Page 44)

100

101

2 Matrices and Arra ys

condition estimate,isontheorderofeps , the floating-point relative precision,

so the computed inverse is unlikely to be of much use.

Theeigenvaluesofthemagicsquareareinteresting:

e = eig(A)

34.0000

8.0000

0.0000

-8.0000

One of the eigenvalues is zero, which is another co ns eque nce of singularity.

The largest eigenvalue is 34, the magic sum. That is because the vector of all

ones is an eigenvector:

v = ones(4,1)

A*v

ans =

When a magic square is scaled by its magic sum,

P = A/34

the result is a doubly stochastic matrix whose row and column sums are all 1:

0.4706 0.0882 0.0588 0.3824

2-22

1 2 ... 39 40 41 42 43 44 45 46 47 48 49 ... 239 240

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MATLAB POLYSPACE RELEASE NOTES User Manual Page 44

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