The eigenvectors-eigenvalues identity and Sun's conjectures on determinants and permanents
نویسندگان
چکیده
In this paper, we prove several conjectures raised by Zhi-Wei Sun on determinants and permanents the eigenvectors-eigenvalues identity recently highlighted Denton, Parke, Tao Zhang.
منابع مشابه
Notes on Eigenvalues and Eigenvectors
Exercise 4. Let λ be an eigenvalue of A and let Eλ(A) = {x ∈ C|Ax = λx} denote the set of all eigenvectors of A associated with λ (including the zero vector, which is not really considered an eigenvector). Show that this set is a (nontrivial) subspace of C. Definition 5. Given A ∈ Cm×m, the function pm(λ) = det(λI − A) is a polynomial of degree at most m. This polynomial is called the character...
متن کاملOn eigenvalues and eigenvectors of subdirect sums
Some new properties of the eigenvalues of the subdirect sums are presented for the particular case of 1-subdirect sums. In particular, it is shown that if an eigenvalue λ is associated with certain blocks of matrix A or matrix B then λ is also an eigenvalue associated with the 1-subdirect sum A ⊕1 B. Some results concerning eigenvectors of the k-subdirect sum A⊕k B for an arbitrary positive int...
متن کاملLecture 8 : Eigenvalues and Eigenvectors
Hermitian Matrices It is simpler to begin with matrices with complex numbers. Let x = a + ib, where a, b are real numbers, and i = √ −1. Then, x∗ = a− ib is the complex conjugate of x. In the discussion below, all matrices and numbers are complex-valued unless stated otherwise. Let M be an n× n square matrix with complex entries. Then, λ is an eigenvalue of M if there is a non-zero vector ~v su...
متن کاملEigenvalues, Eigenvectors, and Sundry Decompositions
We continue with F being an arbitrary field and V a finite dimensional vector space over F ; dimV = n. Conditions on F may be added later on. We assume T ∈ L(V ). Definition 1 We say that an element λ ∈ F is an eigenvalue of T iff there exists x ∈ V , x ̸= 0 such that Tx = λx. We call x ∈ V , x ̸= 0 such that Tx = λx an eigenvector of T , corresponding to the eigenvector λ. If λ is an eigenvector...
متن کاملthe crisis of identity in jhumpa lahiris fiction: interpreter of maladies and the namesake
شکل گیری هویت(identity) مقوله مهمی در ادبیات پراکنده مردم(diasporan literature) می باشد. آثار جومپا لاهیری(jhumpa lahiri) ، نویسنده هندی آمریکایی، در سالهای اخیر تحسین منتقدین را به خود معطوف کرده است. وی در این آثار زندگی مهاجران و تلاش آنان برای پیدا کردن جایگاهشان در یک فرهنگ بیگانه را به تصویر کشیده است. این تجربه همواره با احساساتی نظیر دلتنگی برای گذشته، بیگانگی و دوری همراه است. با این ح...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear & Multilinear Algebra
سال: 2023
ISSN: ['0308-1087', '1026-7573', '1563-5139']
DOI: https://doi.org/10.1080/03081087.2023.2172380