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A tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.

2 votes
1 answer
576 views

Using permutation matrix to convert a matrix into tridiagonal matrix [closed]

Let $A \in \mathbb{R}^{n \times n}$ be a bidiagonal matrix with non zero elements on its diagonal and super diagonal. Let $B$ be defined as $$B=\begin{bmatrix}0&{A} \\{A}^T &0 \end{bmatrix}$$. Find …
1 vote
1 answer
287 views

Relation between the algebraic multiplicity of an eigenvalue and the subdiagonal elements of... [closed]

Show that if $T$ is a symmetric tridiagonal matrix and an eigenvalue $\lambda$ has multiplicity $k$, then at least $k−1$ subdiagonal elements of $T$ are zero. If we consider a submatrix $B$ that …