I have a symmetric matrix that looks like this. (Note that they are not the normal tridiagonal matrices, the diagonals are one diagonal apart). It would be a fairly large matrix. What would be some faster algorithms to diagonalize this?
2026-03-31 14:24:24.1774967064
How to diagonalize this (close-to-diagonal) matrix fast?
78 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in NUMERICAL-LINEAR-ALGEBRA
- sources about SVD complexity
- Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$
- Finding $Ax=b$ iteratively using residuum vectors
- Pack two fractional values into a single integer while preserving a total order
- Use Gershgorin's theorem to show that a matrix is nonsingular
- Rate of convergence of Newton's method near a double root.
- Linear Algebra - Linear Combinations Question
- Proof of an error estimation/inequality for a linear $Ax=b$.
- How to find a set of $2k-1$ vectors such that each element of set is an element of $\mathcal{R}$ and any $k$ elements of set are linearly independent?
- Understanding iterative methods for solving $Ax=b$ and why they are iterative
Related Questions in MATRIX-DECOMPOSITION
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- Swapping row $n$ with row $m$ by using permutation matrix
- Block diagonalizing a Hermitian matrix
- $A \in M_n$ is reducible if and only if there is a permutation $i_1, ... , i_n$ of $1,... , n$
- Simplify $x^TA(AA^T+I)^{-1}A^Tx$
- Diagonalize real symmetric matrix
- How to solve for $L$ in $X = LL^T$?
- Q of the QR decomposition is an upper Hessenberg matrix
- Question involving orthogonal matrix and congruent matrices $P^{t}AP=I$
- Singular values by QR decomposition
Related Questions in DIAGONALIZATION
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Show that $A^m=I_n$ is diagonalizable
- Simultaneous diagonalization on more than two matrices
- Diagonalization and change of basis
- Is this $3 \times 3$ matrix diagonalizable?
- Matrix $A\in \mathbb{R}^{4\times4}$ has eigenvectors $\bf{u_1,u_2,u_3,u_4}$ satisfying $\bf{Au_1=5u_1,Au_2=9u_2}$ & $\bf{Au_3=20u_3}$. Find $A\bf{w}$.
- Block diagonalizing a Hermitian matrix
- undiagonizable matrix and annhilating polynom claims
- Show that if $\lambda$ is an eigenvalue of matrix $A$ and $B$, then it is an eigenvalue of $B^{-1}AB$
- Is a complex symmetric square matrix with zero diagonal diagonalizable?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
This is just two actual tridiagonal matrices interleaved. Permute the rows and columns so that the lines of odd index are in one group and the lines of even index are in another, then use a tridiagonal matrix diagonalisation algorithm on each block.