28 нояб. 2017 г. · Let A have eigenvalue e and eigenvector v, then scale v to have unit norm, i.e. vHv=1 v H v = 1 . Now clearly Av=ev A v = e v and therefore ...

21 июл. 2020 г. · In general, a real matrix has at least one real eigenvector for each eigenvalue. We can sketch out that argument now, using standard theorems about matrices ...

16 окт. 2021 г. · Yes, there is a method called the Sylvester's Criterion. It involves checking the determinants of the principal minors of the matrix. If all ...

12 мая 2024 г. · Yes, it is true. If A A is a symmetric n×n n × n matrix with real entries, then it has n n real eigenvalues {λ1,…,λn} { λ 1 , … , λ n } ...

2 мая 2023 г. · To find a symmetric 2 x 2 matrix with eigenvalues 2 and -4 and the corresponding eigenvectors [1,2] and [2,-1], we can use the formula for ...

7 окт. 2023 г. · Use the fact that for any vector v, (A^2)v = A(Av). Two more lines should give a simple equation for the eigenvalue. Solve the equation.

22 янв. 2022 г. · If your matrix is Hermitian (equal to its conjugate transpose), then by the spectral theorem all the eigenvalues must be real.

7 авг. 2019 г. · Real symmetric matrices are simply Hermitian matrices with all entries real, therefore the result also applies to them.

8 мар. 2021 г. · The eigenvalues, λ± of a 2x2 matrix can be written λ±=(T±√(T2−4Δ))/2 λ ± = ( T ± ( T 2 − 4 Δ ) ) / 2 where T and Δ are the trace and ...

14 янв. 2021 г. · For example, if the matrix has real components and is symmetric, it will have real eigenvalues. There are certainly non-symmetric matrices that ...