7 Eigenvalues and Eigenvectors

2016年9月21日 — In a Hermitian Matrix, the Eigenvectors of Different Eigenvalues are Orthogonal ... This is an elementary (yet important) fact in matrix analysis.

2014年4月21日 — Let's write the problem in a better way. You have a Hermitian matrix A, two distinct eigenvalues λ and μ and two eigenvectors v≠0, ...

2013年10月15日 — Let L be a linear operator on some given vector space V . A scalar λ and a nonzero vector v are referred to, respectively, as an eigenvalue and ...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in ...

Spectral theorem for unitary matrices. For a unitary matrix,. (i) all eigenvalues have absolute value 1,. (ii) eigenvectors corresponding to distinct ...

The eigenvalues and eigenvectors of Hermitian matrices have some special properties. First of all, the eigenvalues must be real!

2017年2月24日 — M is Hermitian iff all its eigenvalues are real. If further M is real and symmetric, then all its eigenvectors have real entries as well.

2017年9月14日 — Consider a Hermitian matrix M=M†. Clearly, its eigenvalues are real, but what is the condition for the eigenvectors to be real as well?