Practice Problems on Trace of a Matrix

1. Given the matrix , calculate the trace of matrix A.

2. Find the trace of the matrix

3. Given the diagonal matrix compute the trace of matrix C

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 β€œm by n” matrix when it has β€œm” rows and β€œn” columns and is written as an β€œm Γ— n” matrix. For example, if a matrix has three rows and four columns, then the order of the matrix is β€œ3 Γ— 4.” 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.

Similar Reads

What is a Square Matrix?

Before learning the concept of the trace of a matrix, we need to know about a square matrix. A square matrix is defined as a matrix with an equal number of rows and columns. For example, if the order of a square matrix is β€œ3 Γ— 3,” then it has three rows and three columns....

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 β€œn Γ— n.” Let us consider a square matrix of order β€œ3 Γ— 3,” as shown in the figure given below, a11, a12, a13,…, a32, and a33 are the entries of the given matrix A. Now, the trace of matrix β€œA” is equal to the sum of its principal diagonal elements, i.e., a11, a22, and a33....

Trace of a Matrix Properties

The following are some important properties of a trace of a matrix. Let us consider two square matrices A and B of the same order....

Trace of a Matrix Examples

Example 1: Prove that the trace of an identity matrix of order β€œ3 Γ— 3” is 3....

Practice Problems on Trace of a Matrix

1. Given the matrix , calculate the trace of matrix A....

Trace of a Matrix – FAQs

What is a square matrix?...