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The Triangular Decomposition(LL~T) of the Positive Semidefinite Symmetric Real Matrix

Yuan Li

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Abstract

Let n×n be positive semi definite symmetric real matrix.It is called triangular decomposition of matrix A if A=LL T ,Matrix L is a lower triangular matrix whose elements on diagnal line are noanegative.In this paper,discussed is the existence and a necessary and sufficient condition of the triangular decomposition uniqueness,and then presented is algorithm of the triangular decompsition of the positive semi definite symmetric real matrix.

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What this paper is about

Let n×n be positive semi definite symmetric real matrix.It is called triangular decomposition of matrix A if A=LL T ,Matrix L is a lower triangular matrix whose elements on diagnal line are noanegative.In this paper,discussed is the existence and a necessary and sufficient condition of the triangular decomposition uniqueness,and then presented is algorithm of the triangular decompsition of the positive semi definite symmetric real matrix.

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Available abstract

Let n×n be positive semi definite symmetric real matrix.It is called triangular decomposition of matrix A if A=LL T ,Matrix L is a lower triangular matrix whose elements on diagnal line are noanegative.In this paper,discussed is the existence and a necessary and sufficient condition of the triangular decomposition uniqueness,and then presented is algorithm of the triangular decompsition of the positive semi definite symmetric real matrix.

Key concepts: Positive-definite matrix, Triangular matrix, Symmetric matrix, Mathematics, Matrix (chemical analysis), Uniqueness, Combinatorics, Band matrix

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