# Questions tagged [tridiagonal-matrices]

Relating to all $n\times n$ matrices $(A)$ with the property $a_{i,j}=0$ if $|j-i|>1$

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### How to show two matrices are similar? [closed]

Show that the matrices A = ⎡ 1 1 1 ⎤ ⎢ 1 1 1 ⎥ ⎣ 1 1 1 ⎦ and B = ⎡ 3 0 0 ⎤ ⎢ 0 0 0 ⎥ ⎣ 0 0 0 ⎦ are similar? I know I should show there exist P- such that A=PBP-, but how do I find P, and is there a ...
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### Recursive computation of determinant of Toeplitz tridiagonal matrix

Let a matrix be a tridiagonal matrix of size $n \times n$, with elements equal to $2$ on the main diagonal, elements equal to $1$ directly above the main diagonal, elements equal to $3$ directly below ...
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Let $a_k(t), b_k (t) \in \mathbb{R} \ (k = 1, 2, \dots, n)$ satisfy the following differential equations: \begin{aligned} \dot a_k(t) &= 2 \left( b_k^2 - b_{k-1}^2 \right) \\ \dot b_k(t) &= ... 0 votes 0 answers 17 views ### Decomposition of stochastic matrices into tridiagonal ones I was wondering if some results were known for the following problem for which I couldn't find any information, except for this similar question that unfortunately doesn't have answers. So let's start ... 3 votes 2 answers 124 views ### Toeplitz tridiagonal matrix with 0s on main diagonal and 1s on sub/superdiagonal has distinct eigenvalues [closed]\begin{pmatrix}0&1&&&\\ 1&\ddots&\ddots&&\\ &\ddots&\ddots&\ddots&\\ &&\ddots&\ddots&1\\ &&&1&0\end{pmatrix}$$has ... 1 vote 2 answers 88 views ### Can this 3 \times 3 tridiagonal Toeplitz matrix be rank-1? I am trying to determine whether the following tridiagonal 3 \times 3 matrix can have a rank of 1.$$\begin{bmatrix}a&b&0\\b&a&b\\0&b&a\end{bmatrix}$$For a = b = 0, the ... 0 votes 0 answers 64 views ### Wilkinson's matrix eigengap Task The (2n+1) \times (2n+1) Wilkinson matrix is a symmetric tridiagonal matrix whose main diagonal is$$n, n-1, \ldots, 1, 0, 1, \ldots, n$$and whose entries on the first diagonals above and ... 0 votes 0 answers 33 views ### the spectrum of tridiagonal matrix is bounded What is the smallest eigenvalue of this infinite, symmetric, tridiagonal matrix? how could I prove that tridiagonal matrix have the smallest eigenvalue，and for any 𝜆 , the spectrum of that matrix is ... 2 votes 1 answer 90 views ### How to notate off-diagonal blocks for a tridiagonal block matrix I have a block diagonal matrix that also has partitioned identity matrices in the off-diagonal blocks, like a tridiagonal block matrix. It looks something like$$ \begin{bmatrix} \textbf{A} & I &...
Let $A\in\mathbb{R}^{n\times n}$ be the symmetric tridiagonal matrix \begin{equation*} A:=\begin{pmatrix} u_1 & v_1 & \\ v_1 & u_2 & v_2 \\ & v_2 & \ddots & \ddots \\ &...