norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field  ...

{R} ^{m},} then the matrix norm given to a matrix A {\displaystyle A} is the square root of the largest eigenvalue of the matrix A ∗ A {\displaystyle...

identity matrix, this norm corresponds to the Euclidean norm. If A {\displaystyle A} is diagonal, this norm is also called a weighted norm. The energy norm is...

infimum of all norms of a matrix. Indeed, on the one hand, ρ ( A ) ⩽ ‖ A ‖ {\displaystyle \rho (A)\leqslant \|A\|} for every natural matrix norm ‖ ⋅ ‖ {\displaystyle...

addition, the Frobenius norm and the trace norm (the nuclear norm) are special cases of the Schatten norm. The singular values of a matrix ⁠ A {\displaystyle...

choice of norm, as can be illustrated by two examples. If ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is the matrix norm induced by the (vector) Euclidean norm (sometimes...

\left(A_{n}\right)} ⁠ converges to the matrix ⁠ A {\displaystyle A} ⁠ (in the maximum norm or Frobenius norm, say), then ⁠ ( A n ) + {\displaystyle (A_{n})^{+}}...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

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...

matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes...

the matrix measure or the Lozinskiĭ measure. Let A {\displaystyle A} be a square matrix and ‖ ⋅ ‖ {\displaystyle \|\cdot \|} be an induced matrix norm. The...

then the corresponding matrix series converges for matrices A such that ‖ A ‖ < r {\displaystyle \|A\|<r} for some matrix norm that satisfies ‖ A B ‖...

the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

size to any vector in a vector space Matrix norm, a map that assigns a length or size to a matrix Operator norm, a map that assigns a length or size to...

the same as Schatten norm. In fact, we have ‖ A ‖ matrix p-norm , 2 = ‖ A ‖ Schatten , ∞ {\displaystyle \|A\|_{{\text{matrix p-norm}},2}=\|A\|_{{\text{Schatten}}...

normal operators on infinite-dimensional normed spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved...

particular matrix. The norm of a matrix is a positive real number. For all matrices A and B in Mmn(F), and all numbers α in F, a matrix norm, delimited...

{\displaystyle CD} " norm: ‖ A ‖ {\displaystyle \|A\|} , read "the norm (length, size, magnitude etc.) of the matrix A {\displaystyle A} ". The norm of a one-dimensional...

{\displaystyle P} and I − P {\displaystyle I-P} are equal, and thus that the matrix norm of the oblique projections are the same. However, the condition number...

subset of n-by-n matrix units in the set of n-by-n matrices over R. The matrix norm (induced by the same two vector norms) of a matrix unit is equal to...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

example, in the low-rank matrix completion problem one may apply the regularization penalty taking the form of a nuclear norm R ( X ) = λ ‖ X ‖ ∗ {\displaystyle...

greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix that may also be referred to as Smith's matrix. The study was initiated...

the matrix is very small. The norm of a matrix can be used to capture the conditioning of linear algebraic problems, such as computing a matrix's inverse...

the matrix condition number κ(A−1, b) is given by ||A||op||A−1||op, where || ||op is the operator norm subordinate to the normal Euclidean norm on Cn...

vector n-norm or matrix norm. Common examples of such norms include the L1 norm (sum of absolute component values), the L2 norm (Euclidean norm, or square...

{\displaystyle n} goes to infinity, the matrix norm of C {\displaystyle C} must be smaller than unity. This norm is | | C | | ∞ = max i ∑ j | c i j | =...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a...

in the Matrix franchise to be directed solely by Lana. It is the sequel to The Matrix Revolutions (2003) and the fourth installment in The Matrix film series...