What is symmetric band?

A symmetric band matrix is a symmetric matrix whose nonzero elements are arranged uniformly near the diagonal, such that: aij = 0 if |i-j| > k. where k is the half band width.

What is banded matrix in FEM?

In numerical analysis, matrices from finite element or finite difference problems are often banded. Such matrices can be viewed as descriptions of the coupling between the problem variables; the banded property corresponds to the fact that variables are not coupled over arbitrarily large distances.

What are the types of band matrix?

A general band matrix has nonzero elements both above and below the main diagonal. An upper band matrix only has elements on and above the main diagonal. A lower band matrix has elements on and below the main diagonal. A symmetric band matrix has identical elements on either side of the main diagonal.

What is semi bandwidth?

The left half-bandwidth of is defined as the smallest positive integer such that whenever . In other words, entries that are more than positions below the main diagonal are zero. The right half-bandwidth of is defined as the smallest positive integer such that whenever .

Are matrices symmetric?

A square matrix that is equal to the transposed form of itself is called a symmetric matrix. Since all off-diagonal elements of a square diagonal matrix are zero, every square diagonal matrix is symmetric. The sum of two symmetric matrices gives a symmetric matrix as result.

What is a matrix band?

A metal or plastic band secured around the crown of a tooth to confine the restorative material filling a cavity.

What is matrix bandwidth?

Bandwidth of a matrix A is defined as the smallest non-negative integer K such that A (i, j) = 0 for |i – j| > K. For example, a matrix with all zeros will have its bandwith equal to zero. Similarly bandwith of diagonal matrix will also be zero. For example, for the below given matrix, the bandwith of this matrix is 2.

What is upper and lower bandwidth?

The upper and lower bandwidths of a matrix are measured by finding the last diagonal (above or below the main diagonal, respectively) that contains nonzero values. That is, for a matrix A with elements Aij: The upper bandwidth B1 is the smallest number such that A i j = 0 whenever j − i > B 1 .

What defines a symmetric matrix?

A matrix is symmetric if and only if it is equal to its transpose. All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal.

What is a symmetrical shape?

Symmetry. A 2D shape is symmetrical if a line can be drawn through it and either side is a reflection of the other. The line is called a line of symmetry. This is sometimes called a ‘mirror line’ or ‘mirror symmetry’, because if you put a mirror on the line, the reflection would show the whole shape.

Can stiffness matrix be asymmetrical?

I was under the impression that mass and stiffness matrices are always symmetric (as I have been taught in my course and in textbook as well) but while solving questions from another textbook, I came to know that the matrices can be asymmetric as well.

Where is a universal matrix band used?

Class II restorations
Matrix Band Placement The Universal (Tofflemire) matrix system is used in Class II restorations. The primary function of the matrix is to restore anatomic proximal contours and contact areas.

What is meant by semi bandwidth?

The right half-bandwidth of is defined as the smallest positive integer such that whenever . In other words, entries that are more than positions above the main diagonal are zero. The banwidth is defined as , where are the left and right half-bandwidths respectively.

What is symmetric and asymmetric matrix?

A symmetric matrix and skew-symmetric matrix both are square matrices. But the difference between them is, the symmetric matrix is equal to its transpose whereas skew-symmetric matrix is a matrix whose transpose is equal to its negative.

What is symmetrical example?

Symmetry is defined as a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half. For example, different shapes like square, rectangle, circle are symmetric along their respective lines of symmetry.

Is flexibility matrix symmetric?

1.4. The flexibility matrix, [α], is also symmetric, and its individual terms are known as flexibility influence coefficients.

Why is stiffness matrix symmetric?

The stiffness matrix is symmetric if the operator L of the PDE is self-adjoint, i.e. if you have ⟨Lf,g⟩=⟨f,Lg⟩ for any pair of functions (f,g) in the suitable function space, where ⟨u,v⟩ denotes the inner product between two functions u,v, for instance ∫Ωuvdx (L2 inner product).