How to create positive semidefinite matrix from random value ?

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?

Answer 1

[Walter Roberson]

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