Positive-definite matrix
= Positive-definite matrix
A real symmetric matrix $A$ is positive definite when
$$
x^TAx>0
$$
for every nonzero real <vector> $x$. It therefore defines the <inner product> $\langle x,y\rangle_A=x^TAy$ and is invertible.
= Positive-definite matrix
A real symmetric matrix $A$ is positive definite when
$$
x^TAx>0
$$
for every nonzero real <vector> $x$. It therefore defines the <inner product> $\langle x,y\rangle_A=x^TAy$ and is invertible.