Matrix whose only nonzero elements are on its main diagonal
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it is a diagonal matrix called scalar matrix, for example, .
In geometry, a diagonal matrix may be used as a scaling matrix, since matrix multiplication with it results in changing scale (size) and possibly also shape; only a scalar matrix results in uniform change in scale.
In linear algebra, a diagonalmatrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...
linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonalmatrix. That is, if there exists...
A block diagonalmatrix is a block matrix that is a square matrix such that the main-diagonal blocks are square matrices and all off-diagonal blocks are...
tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this)...
adopted into Latin as diagonus ("slanting line"). In matrix algebra, the diagonal of a square matrix consists of the entries on the line from the top left...
Every square diagonalmatrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of...
where Q is the square n × n matrix whose ith column is the eigenvector qi of A, and Λ is the diagonalmatrix whose diagonal elements are the corresponding...
the main diagonal of a square matrix. They lie on the imaginary line which runs from the top left corner to the bottom right corner of the matrix. For instance...
also called a heavy node, results in a large diagonal entry in the Laplacian matrix dominating the matrix properties. Normalization is aimed to make the...
mathematics. A matrix M is positive-definite if and only if it satisfies any of the following equivalent conditions. M is congruent with a diagonalmatrix with...
spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonalmatrix, and therefore any matrix A satisfying the equation...
long as diagonally-opposite entries are complex conjugates. A matrix that has only real entries is symmetric if and only if it is a Hermitian matrix. A real...
mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is greater...
matrices, the diagonalmatrix, is to store just the entries in the main diagonal as a one-dimensional array, so a diagonal n × n matrix requires only...
which for a matrix is the conjugate transpose. The product of a matrix with its adjugate gives a diagonalmatrix (entries not on the main diagonal are zero)...
lower triangular with ones on the diagonal, U is upper triangular with ones on the diagonal, and D is a diagonalmatrix. Related: the LUP decomposition...
of j-th column of the matrix A. Yet, there is a special basis for an operator in which the components form a diagonalmatrix and, thus, multiplication...
square root matrix of D, which, for distinct eigenvalues, must be diagonal with diagonal elements equal to square roots of the diagonal elements of D;...
the main diagonal are called diagonal matrices. The eigenvalues of a diagonalmatrix are the diagonal elements themselves. Consider the matrix A = [ 1...
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...
square (N × N) matrix whose ith column is the eigenvector q i {\displaystyle q_{i}} of A, and Λ is the diagonalmatrix whose diagonal entries are the...
matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal...
where I is the n×n identity matrix. When X is an n×n diagonalmatrix then exp(X) will be an n×n diagonalmatrix with each diagonal element equal to the ordinary...
matrix that describes adjacency in bipartite graphs. Degree matrix — a diagonalmatrix defining the degree of each vertex in a graph. Edmonds matrix —...
algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A {\displaystyle...
triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly...
semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). The covariance matrix of a random vector X {\displaystyle...
Global Information![{\displaystyle \left[{\begin{smallmatrix}3&0\\0&2\end{smallmatrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd1681ed0048aa1b28a2e9b5f6bb834b1cc3b14)
![{\displaystyle \left[{\begin{smallmatrix}6&0&0\\0&5&0\\0&0&4\end{smallmatrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bad34bc0da45cc29d4095720a4a8c9b2cac2a26)
![{\displaystyle \left[{\begin{smallmatrix}0.5&0\\0&0.5\end{smallmatrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae9d50cf77850fc91f92a367564eafc7f1f4718)