Latest update

- Interface Microsoft Access to Drupal database
- Do Intel, NVIDIA and AMD have a financially good reason to intentionally cripple hardware in order to alter the prices of their range of pro
- Did Trump say that laziness is a Black trait?
- “Dusty Corners of the Market”
- option price change
- Max Heap Data Structure Implemented with Python List
- Simple implementation of nxn Dense Matrix in Java
- JS Procedural Hangman
- Unit test for class converting between DTOs and entities
- Converting graphviz (dot) files to mxGraph (draw.io) files
- Looking for a Sci Fi story - mining colony with robots?
- Where did Percy sleep when he was away from the Weasleys?
- Soundtrack (background music) Stargate SG-1 9x06 (Beachhead)
- sf apocalyptic short story probably from the 50s
- In Twilight, could the vampire head still live if only the body was burned?
- Left join with WHERE (microsoft access SQL)
- What Happens to dirty pages if the system fails before the next checkpoint?
- Photoshop - slice and save image - can't get save dialog. Has something changed?
- what graphic designing tool is used by big platforms like Facebook & Google?
- Looking for Photoshop script to batch replace all black portions into green color in all images in a folder?

# Tridiagonal matrix with charcteristic polynomial is a polynomial $T_k(x)$ given recursively

2017-12-14 05:24:12

Let the polynomial sequence $T_k(x)$ as follow:

$T_0(x)=1$, $T_1(x)=x$ and $T_{n+1}(x)=2xT_n(x)-T_{n-1}(x)$ for all $n\geq 1$.

Show the following:

1) For every $n\geq 2$ find a tridiagonal matrix $A_n$ so that its characteristic polynomial is $T_n(x)$.

2) Show that $A_n$ is similar to symmetric tridiagonal matrix.

The symmetric tridiagonal are the matrix in this link https://en.wikipedia.org/wiki/Tridiagonal_matrix

I showed one recursive formula for the polynomial characteristic of a tridiagonal matrix but i not can using this for to show the points 1 and 2 before.

I wait that can you help me with hints or any thing...