Linear span – Knowledge and References

Linear span

Linear span refers to the set of all possible linear combinations of a given set of vectors that are of the same dimension. It is denoted by the symbol and is a subset of the vector space X. The dimension of X is used to determine the number of vectors needed to span the space, and the linear span of a subset S is written as ~~.From: Introduction to Machine Learning with Applications in Information Security [2017], A framework for solving mixed-integer semidefinite programs [2018]~~

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Principal Components of Principal Component Analysis

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Published in Mark Stamp, Introduction to Machine Learning with Applications in Information Security, 2017

Mark Stamp

Given a set of vectors that are all of the same dimension, the span, or linear span, of these vectors consists of all linear combinations of the vectors, that is, all sums of scalar multiples. For example, given xn×1, yn×1, and zn×1, any vector that can be written as αx + βy + γz

Linear Algebra

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Published in Richard L. Shell, Ernest L. Hall, Handbook of Industrial Automation, 2000

William C. Brown

Definition 18. Let S be a subset of a vector space V. The set of all linear combinations of vectors from S is called the linear span of S. We will let L(S)denote the linear span of S.

A framework for solving mixed-integer semidefinite programs

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Published in Optimization Methods and Software, 2018

Tristan Gally, Marc E. Pfetsch, Stefan Ulbrich

Moreover, is the ith unit vector in . For a vector space X, is its dimension, and for some subset , the linear span is written as . The range of an operator is denoted by , and the preimage of is given by .