Is this matrix a positive or semi-positive definite matrix ?
[ 2 0 0 0
0 2 0 0
0 0 2 0
0 0 0 0 ]
Konstantin K. Avilov
The matrix is semi-positive, but not positive.
Let:
A=[ 2 0 0 0
0 2 0 0
0 0 2 0
0 0 0 0 ],
x=[a
b
c
d]
with a,b,c,d being complex numbers.
Then: q=conj(x)*A*x=2*(|a|^2+|b|^2+|c|^2)
It is obvious that q>=0 for any a,b,c,d (hence, A is semi-positive), but when d=1 and a=b=c=0 we have q=0 (hence, A is NOT positive).
1 votes
1 thanks
Pietro Piu
Both eigendecomposition and Cholevsky decomposition show that the given matrix is not positive definite.
1 votes
1 thanks
R. C. Mittal
Yes positive semi-definite, because all eigen values are non- negative.Being diagonal matrix, eigen-values are 2,2,2,0.
0 votes
0 thanks
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix
More Abdullah Waseem's questions See All
Similar questions and discussions