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2002•Journal of Tianjin Normal UniversityRequires access

Generalized Trace of a Matrix

Jian Mao

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Abstract

In this paper we present the concept of the generalized trace of a square matrix, which is a natural generalization of the concept of the matrix trace,and discuss the properties of the generalized trace of a matrix and its recursive method of calculation. The main of all the results is as follows, the k order generalized trace of a matrix is equal to the elementary symmetrical polynomial of degree k in all eigenvalues of the matrix.

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What this paper is about

In this paper we present the concept of the generalized trace of a square matrix, which is a natural generalization of the concept of the matrix trace,and discuss the properties of the generalized trace of a matrix and its recursive method of calculation. The main of all the results is as follows, the k order generalized trace of a matrix is equal to the elementary symmetrical polynomial of degree k in all eigenvalues of the matrix.

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Available abstract

In this paper we present the concept of the generalized trace of a square matrix, which is a natural generalization of the concept of the matrix trace,and discuss the properties of the generalized trace of a matrix and its recursive method of calculation. The main of all the results is as follows, the k order generalized trace of a matrix is equal to the elementary symmetrical polynomial of degree k in all eigenvalues of the matrix.

Key concepts: TRACE (psycholinguistics), Generalization, Matrix (chemical analysis), Square matrix, Mathematics, Eigenvalues and eigenvectors, Single-entry matrix, Matrix function

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