Matrix Norm
Want to read more about matrix norms since I have read about Recommender systems and I utilize embeddings for this site.
Date Created:
2
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References
Related
- norms
- In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself.
- commutes
- In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation.
- triangle inequality
- In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
- vector space
- In mathematics and physics, a vector space (also called a linear space) is a ser whose elements, often called vectors, can be added together and multiplied (
scaled
) by numbers called scalars. Th operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field.
- In mathematics and physics, a vector space (also called a linear space) is a ser whose elements, often called vectors, can be added together and multiplied (
- Euclidean Vectors
- In mathematics, physics, and engineering, a Euclidean vector or simply a vector is a geometric object that has magnitude and direction. Euclidean vectors can be added and scaled to form a vector space.
Notes
In the field of mathematics, norms are defined for elements within a vector space. Specifically, when the vector space comprises matrices, such norms are referred to as matrix norms. Matrix norms differ form vector norms in that they must interact with matrix multiplication.
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