Yanjun Li
Abstract
Let S_n(R)be the space of all n×n symmetric matrices over real fields.For a function f:S_n(R)→S_n(R),if rankA=ranf(A),(?)A∈S_n(R),then f is called a function preserving rank of symmetric matrices.In this paper,we characterize the functions of preserving rank on symmetric matrices when n≤3.
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Let S_n(R)be the space of all n×n symmetric matrices over real fields.For a function f:S_n(R)→S_n(R),if rankA=ranf(A),(?)A∈S_n(R),then f is called a function preserving rank of symmetric matrices.In this paper,we characterize the functions of preserving rank on symmetric matrices when n≤3.
Key concepts: Rank (graph theory), Mathematics, Combinatorics, Matrix (chemical analysis), Symmetric space, Function (biology), Symmetric function, Symmetric matrix