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M = [ 1.0000 0 0 0 0 0;...

0 0.9803 -0.0000 -0.0000 -0.0984 0.0984;...

0 -0.0000 0.9902 -0.0984 0.0000 0.0000;...

0 -0.0000 -0.0984 0.0098 0.0000 -0.0000;...

0 -0.0984 0.0000 0.0000 0.0099 -0.0099;...

0 0.0984 0.0000 -0.0000 -0.0099 0.0099];

Is from and its eigenvalues are

d =

-0.0000

-0.0000

0.0000

1.0000

1.0000

1.0000 =

%When vpa is used it shows

-7.365e-18

-2.12e-18

1.347e-16

1.0

1.0

1.0

So, can't we call matrix M, positive semidefinite ?

Apperciated!

Matt J
on 22 Oct 2020

Edited: Matt J
on 22 Oct 2020

Matt J
on 22 Oct 2020

It is very easy to prove from the definition of positive semidefiniteness

x.'*(A*A.')*x

=(x.'*A)*(A.'*x)

=(A.'*x).' * (A.'*x)

=dot(A.'*x,A.'*x)

>=0

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