Relationship Between Hermitian and Symmetric Matrices

[math_major_111]

Are All symmetric matrices with real number entires Hermitian? What about the other way around-are all Hermitian matrices symmetric?

 

[PeterDonis]

Are All symmetric matrices with real number entires Hermitian?

What do you get when you take the conjugate transpose of a symmetric matrix with all real entries? Have you tried it?

What about the other way around-are all Hermitian matrices symmetric?

Are you this time including Hermitian matrices with complex (nonzero imaginary part) entries?

 

[fresh_42]

What is a Hermitian matrix, and what does this mean, if all entries were real?

 

[PeterDonis]

What is a Hermitian matrix, and what does this mean, if all entries were real?

A Hermitian matrix is a matrix that is equal to its conjugate transpose, i.e., $H = H^{\dagger}$.