# 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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### $\|\cdot\|_2$ norm of tridiagonal matrix

Let $T\in M_{n}(\mathbb{R})$ be a tridiagonal matrix. What can we say about operator norm $\|T\|_2$? I'm asking this question because we know that if $T$ were only diagonal, then $\|T\|_2$ is the ...
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### Eigenvalues of a particular tridiagonal matrix with a variation on one of its diagonal entries

I am trying to obtain the eigenvalues of this particular $n\times n$ tridiagonal matrix \begin{eqnarray} A & = & \begin{bmatrix} 1+a^{2} & -a & 0 & \ldots & 0 & 0 \\ -a ...
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### Creating a Tridiagonal Matrix given 2 Vectors in Matlab

I'm new to Matlab (coming from Python), and I'm trying to figure out the following matrix $A$ given 2 input arrays, $a = [a_0, a_1, ... , a_{n-1}]$, and $b = [b_1, b_2, ... , b_n]$. I tried ...
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### What real-life examples of a Tridiagonal matrix are there?

I've been looking into the Tridiagonal matrix algorithm. There's theory everywhere but not a lot of real-world applications and examples of tridiagonal matrices. I understand it is a pretty simple and ...
Let $n\times n$ complex matrices $A=(a_{ij})_{1\leq i,j\leq n}$ and $B=(b_{ij})_{1\leq i,j\leq n}$ be a tri-diagonal matrix whose off-diagonal entries are non-zero and a diagonal matrix, respectively. ...
Consider the matrix A_n=\begin{bmatrix} a & b & 0 & 0 & 0 & \dots & 0 & 0 & 0 \\ c & a & b & 0 & 0 & \dots & 0 & 0 & 0 \\ 0 & c ...