## What is tridiagonal matrix with example?

A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal. The set of all n × n tridiagonal matrices forms a 3n-2 dimensional vector space.

## How do you solve a tridiagonal matrix?

The system can be efficiently solved by setting Ux = ρ and then solving first Lρ = r for ρ and then Ux = ρ for x. The Thomas algorithm consists of two steps. In Step 1 decomposing the matrix into M = LU and solving Lρ = r are accomplished in a single downwards sweep, taking us straight from Mx = r to Ux = ρ.

**What is a symmetric tridiagonal matrix?**

A tridiagonal matrix A is also symmetric if and only if its nonzero elements are found only on the diagonal, subdiagonal, and superdiagonal of the matrix, and its subdiagonal elements and superdiagonal elements are equal; that is: (aij = 0 if |i-j| > 1) and (aij = aji if |i-j| = 1)

**Is Thomas algorithm an iterative method?**

Explanation: Thomas algorithm solves a system of equations with non-repeated sequence of operations. It is a direct method to solve the system without involving repeated iterations and converging solutions.

### How do you create a circulant matrix in Matlab?

Perform discrete-time circular convolution by using toeplitz to form the circulant matrix for convolution. Define the periodic input x and the system response h . x = [1 8 3 2 5]; h = [3 5 2 4 1]; Form the column vector c to create a circulant matrix where length(c) = length(h) .

### How does Matlab calculate LU decomposition?

[ L , U ] = lu( A ) factorizes the full or sparse matrix A into an upper triangular matrix U and a permuted lower triangular matrix L such that A = L*U . [ L , U , P ] = lu( A ) also returns a permutation matrix P such that A = P’*L*U . With this syntax, L is unit lower triangular and U is upper triangular.

**Are tridiagonal matrices always invertible?**

with a > 0 and a = b. It is very interesting that, under the above conditions, C is always invertible and its inverse is a tridiagonal matrix.

**Which of the following method is not an iterative?**

Which of the following is not an iterative method? Explanation: Jacobi’s method, Gauss Seidal method and Relaxation method are the iterative methods and Gauss Jordan method is not as it does not involves repetition of a particular set of steps followed by some sequence which is known as iteration.

## How to find inverse of 3×3 matrix?

Check the determinant of the matrix.

## Are all real symmetric matrices diagonalizable?

Real symmetric matrices are diagonalizable by orthogonal matrices; i.e., given a real symmetric matrix A, QTAQ is diagonal for some orthogonal matrix Q. More generally, matrices are diagonalizable by unitary matrices if and only if they are normal.

**How to determine the eigenvalues of a matrix?**

Step 1: Make sure the given matrix A is a square matrix. Also,determine the identity matrix I of the same order.

**How do you find the determinant of a matrix?**

Summary. For a 2×2 matrix the determinant is ad-bc. For a 3×3 matrix multiply a by the determinant of the 2×2 matrix that is not in a’s row or column, likewise for b and c, but remember that b has a negative sign!