1 февр. 2022 г. · A matrix A is positive definite if x'Ax > 0 for all non-zero x. If A is symmetric, then the the eigenvalues are real numbers.

8 мар. 2021 г. · It is conceivable for a matrix to have certain eigenvalues that are negative if it is not symmetric, which would go against the notion of a ...

15 мар. 2020 г. · In general, any non-symmetric matrix with positive eigenvalues can be considered non-symmetric positive definite.

18 нояб. 2023 г. · A real nonsymmetric matrix can very well be positive definite in the sense that xTAx>0 x T A x > 0 for each nonzero vector x x .

8 мая 2024 г. · Examples of non-symmetric positive semidefinite matrices can be provided. To prove a symmetric matrix is positive semidefinite, ...

14 янв. 2021 г. · A matrix with negative eigenvalues cannot be positive definite, whether or not it is symmetric. Both conditions are necessary, so to prove “not- ...

17 нояб. 2020 г. · Can a positive definite matrix be non-symmetric? yes, any 2X2 matrix A whose det( A) > 0 can be formed by [a b:c d] ad-bc>0. and b not = c.

11 нояб. 2023 г. · For a non-symmetric matrix to have both positive and negative eigenvalues, it must be a non-normal matrix. Normal matrices are defined as ...

14 июн. 2018 г. · Can a non symmetric real matrix be positive definite? It's not standard terminology, but we can certainly consider not-necessarily-symmetric ...

4 дек. 2021 г. · If a Hermitian matrix has at least one entry with a (nonzero) imaginary part, then the matrix is not symmetric, but it could still be positive ...