MATLAB: How to create positive semidefinite matrix from random value

positive deifinite matrix

I form a matrix A in matlab as
A=rand(50);
I want to know how to make symmetric matrix using equation
A=0.5 *(A+A');
but how can I make it positive semidefinite matrix?

Best Answer

https://www.mathworks.com/matlabcentral/answers/84287-positive-semi-definite-matrix-problem 
A = rand(50);
A = 0.5 *(A+A');
issymmetric(A)
ans = logical
   1

d = eig(A)
d = 50×1
   -2.6403
   -2.3499
   -2.3084
   -2.1472
   -2.0568
   -1.9520
   -1.8574
   -1.5880
   -1.5540
   -1.4120

all(imag(d) == 0 & d >= 0)
ans = logical
   0

APos = A'*A;
issymmetric(APos)
ans = logical
   1

d = eig(APos)
d = 50×1
    0.0000
    0.0048
    0.0360
    0.0436
    0.0506
    0.0978
    0.1031
    0.1715
    0.1725
    0.1929

●
all(imag(d) == 0 & d >= 0)
ans = logical
   1
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