Jordan algebra – Knowledge and References

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Nonassociative Algebras

Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006

Murray R. Bremner, Lucia I. Murakami, Ivan P. Shestakov

A noncommutative Jordan algebra is an algebra satisfying the flexible and Jordan identities. In this definition the Jordan identity may be replaced by any of the identities x2(xy)=x(x2y),(yx)x2=(yx2)x,(xy)x2=(x2y)x.

A wide neighborhood infeasible-interior-point method with arc-search for -SCLCPs

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Journal Information

Published in Optimization, 2018

M. Sayadi Shahraki, H. Mansouri, M. Zangiabadi

By definition, a Jordan algebra has an identity element denoted by e. For any , let k be the smallest positive integer such that the elements in are linearly dependent; k is called the degree of x and is denoted by . The rank of , simply denoted by r, is the maximum of for all . In Euclidean Jordan algebra , the set of squares is a symmetric cone.

An iteration predictor–corrector interior-point method with a new one-norm neighbourhood for symmetric cone optimization

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Published in Optimization, 2022

M. Sayadi Shahraki, H. Mansouri

A Euclidean Jordan algebra is a triple , where is a finite dimensional inner product space over and is a bilinear map mapping satisfying the following conditions: , and where is defined by .