19 мар. 2023 г. · Some authors use more general definitions of definiteness, including some non-symmetric real matrices, or non-Hermitian complex ones.

3 мар. 2022 г. · Why are Positive Definite Matrices symmetric by definition? We can always find non-symmetric matrices satisfying the same inequality xT.

29 мая 2018 г. · I want to show that a function V = x' A x is larger than zero for all nonzero x, however, the matrix A is not symmetric, and everything I find on positive ...

22 янв. 2022 г. · A non-symmetric matrix (B) is positive definite if all eigenvalues of (B+B')/2 are positive. I was wondering why is this statement true.

25 мая 2014 г. · For any space V and any two inner products <> and () on V, there exists a ()-positive definite matrix P such that <x,y>=(x,Py) for all x and y ...

If they're not symmetric, then they won't produce inner products. Inner products appear all over pure and applied math, so it's useful to have an exact ...

24 мар. 2017 г. · This isn't​ true, since there are plenty of matrices with only positive eigenvalues that aren't symmetric and thus aren't positive definite.

12 февр. 2012 г. · Using M+Mt lets you use theorems about symmetric matrices. Or in this case, M+Mt is 2I which is obviously positive definite.

10 янв. 2023 г. · It means it's eigenvalues are positive. For example [1,-1;-1,1]. (Well technically this is positive semidefinite, but you can slightly increase ...

8 нояб. 2021 г. · A positive-definite matrix is one whose eigenvalues are all positive. What is x? x is a vector. What is the benefit of having/assuming a ...