# Matrix congruence

In the answer of to the question Characterization of positive definite matrix with principal minors I saw such assertion: $$Ak=LkDkL∗k \implies Ak$$ is congruent to Dk . Tell me please, why is it right? Matrices are similar when $$A=LDL^-1$$, not $$L*$$, isn't it? And, regarding to another answer, why "if hermitian matrix A is not positive definite, it must possess at least two(???) negative eigenvalues"? Why not only 1? It has some connection with complex field?