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...

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...

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...

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})^{+}}...

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

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...

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

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 = [...

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

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...

{\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...

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 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...

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...

{\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 | =...

Lax equivalence theorem. Stability in this context means that a matrix norm of the matrix used in the iteration is at most unity, called (practical) Lax–Richtmyer...

In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

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...

Hardy space Sobolev space Tsirelson space ba space Uniform norm Matrix norm Spectral radius Normed division algebra Stone–Weierstrass theorem Banach algebra...

In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield. Let K be a field...

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...