Introduction to Matrix Trace Calculator

The trace of a square matrix calculator is an online tool made to find the trace of a matrix of order 2-by-2, 3-by-3 or 4-by-by. It finds the sum of all diagonal elements of a matrix and shows the answer, including possible intermediate steps.

In matrix algebra, many operations are performed on matrices for different purposes. Similarly, the trace of a matrix is used to find the sum of eigenvalues of the given matrix. We introduce the trace of 3x3 matrix calculator that can easily calculate the trace of the matrix without making the problem complex.

How to Calculate Matrix Trace?

The trace of a matrix refers to the sum of the diagonal elements of a square matrix. The matrix trace is strictly defined for square matrix only. The trace of a matrix is related to the eigenvalues of a matrix, because it is equal to the sum of its eigenvalues.

Let A be a square matrix of order n×n , the trace of A can be written as:

$$ tr(A) \;=\; \sum_{i=1}^n \; a_{ii} $$

Where,

tr(A) = Trace of A Matrix

i = The Row and Column Number of Matrix A

a_ii = The Diagonal Entries of A.

In the case of eigenvalues,

$$ tr(A) \;=\; \sum_{i=1}^n \; λ_i $$

Where,

λ = is the eigenvalues of A.

The above formula is used by the trace calculator for matrices.

Example:

If A is matrix of order 2-by-2 denoted by:

$$ A \;=\; \begin{bmatrix} 1 & 4 \\ 2 & 3 \\ \end{bmatrix} $$

Then the trace of A is,

$$ tr(A) \;=\; 1 \;+\; 3 \;=\; 4 $$

So, the trace of the matrix A is 4.

How to use the Trace of a Matrix Calculator?

It is easy to calculate the trace of a matrix by using a matrix trace calculator with steps, because it contains simple steps. These steps are:

1. In the first step, you need to write the number of rows and columns of a matrix in their respective boxes.
2. Now write the values of all entries of the matrix.
3. Or you can use the random button for a random example.
4. Click on the calculate button.

After clicking the calculate button, you will get the answer within a few moments.

Benefits of using a Trace of a 2x2 Matrix Calculator

In mathematics, online tools can make it easier to understand different concepts and methods of solving problems. Similarly, the trace calculator has many benefits for educational purposes. These benefits are:

1. It can quickly execute and find the sum of a matrix's diagonal.
2. It can help you to approximate the sum of eigenvalues.
3. Matrix trace calculator is a free online tool; you need not pay any fee.
4. It has a simple interface which makes it more reliable.
5. It provides a random option so that you can practice with different examples.

How to find a Trace Matrix Calculator?

You can easily find the trace of 4x4 matrix calculator from your desired browser by searching matrix trace step by step calculator. There will be a list of different math tools available on this site. Select the trace calculator. You can also choose any of these tools.