What is Trace of a Matrix?
Trace of a matrix is defined as the sum of the principal diagonal elements of a square matrix. It is usually represented as tr(A), where A is any square matrix of order βn Γ n.β Let us consider a square matrix of order β3 Γ 3,β as shown in the figure given below, a11, a12, a13,β¦, a32, and a33 are the entries of the given matrix A. Now, the trace of matrix βAβ is equal to the sum of its principal diagonal elements, i.e., a11, a22, and a33.
Trace of a Matrix Meaning
If A is a square matrix of order βn Γ n,β then the trace of matrix A is equal to the sum of the main diagonal elements.
tr(A) = a11 + a22 + a33 + β¦+ ann
Trace of a Matrix
Trace of a Matrix: A matrix is defined as a rectangular array of numbers that are arranged in rows and columns. The size of a matrix can be determined by the number of rows and columns in it. A matrix is said to be an βm by nβ matrix when it has βmβ rows and βnβ columns and is written as an βm Γ nβ matrix. For example, if a matrix has three rows and four columns, then the order of the matrix is β3 Γ 4.β We have different types of matrices, such as rectangular, square, triangular, symmetric, etc.
In this article, we will learn about the Trace of a matrix, along with its definition, Trace of a Matrix properties, and Trace of a Matrix examples.