# Questions tagged [circulant-matrices]

For questions regarding circulant matrices, where each row vector is rotated one element to the right relative to the preceding row vector.

106 questions
Filter by
Sorted by
Tagged with
41 views

1 vote
24 views

### Determinant of circulant $(0,1)$ matrices of certain form

I am interested in computing the determinant of the following circulant matrices: let $n=p^k$ for $p$ a prime and $k\in \mathbb{N}$, take $a\in \mathbb{N}$ to be such that $a<p$ and $(a,p)=1$. ...
22 views

### Diagonalize matrix of linear operator

Let $f : \mathbb{C} \to \mathbb{C}$ linear map such $$f(e_{i}) = \begin{cases} e_{i+1} & 1 \leq i<n \\ e_{1} & i=n\end{cases}$$ Diagonalize $f$. Thoughts I know the characteristic ...
9 views

### inverting a tridiagonal circulant matrix with alternating elements

First of all, I want to underline that my knowledge regarding matrices is extremely restricted.. It just so happens that they are popping out everywhere in a recent project of mine. So, in this ...
1 vote
46 views

### Operations with Circulant Matrix using GAP

I am newbie using GAP software. I need to know how to use GAP software for algebraic computations with circulant matrix. Some examples would suffice. Just for clarity Circulant Matrix: In linear ...
62 views

35 views

### results of calculating eigenvalues and eigenvectors of permutation matrix

My question is actually about the derivation of eigenvalues and eigenvectors of the circulant matrix. I am not good at doing that in a straight way, i.e. calculating them with a general form of ...
58 views

72 views

### Diagonalizing a matrix with 4 circulant blocks

I have the following matrix: $$\mathbf{M} = \begin{pmatrix} G_{1}^{(N)} & G_{2}^{(N)} \\ G_{2}^{(N)} & G_{3}^{(N)} \end{pmatrix}$$, where $G^{(N)}_{j}$ are symmetric circulant matrices of size ...
49 views

### The square root of symmetric and circulant matrix is symmetric

Let $A$ a circulant symmetric matrix. From the definition of $\sqrt{A}$ it follows that also $\sqrt{A}$ is symmetric ( and circulant ). How can I show the symmetry without using the concept of ...
43 views

153 views

In my studies of linear algebra, I have encountered this exercise Let $A$ be a circulant matrix defined as $$A_{jl} = \left\{\begin{array}{cc} r_{l-j} & l\ge j, \\ r_{N+l-j} & l<j\... 3 votes 1 answer 87 views ### Showing that these algebras are isomorphic This paper (page 157) diagonalized circulant matrix S like this where \psi is an eigenvalue and \Omega is composed of the eigenvectors as columns:$$ \Omega^{-1}S\Omega = \begin{bmatrix} \psi_0 ...
Question: Hi! Would anyone happen to know an efficient way to compute: $$u^\top [C + D]^{-1},$$ where: $C$ is a square matrix, and is real, positive definite, and circulant $C$ is too large to fit ...