Algebra
Matrix Trace Calculator
Easily calculate the trace of a square matrix online. Enter your matrix and instantly find the sum of its diagonal elements with this user-friendly tool.
Enter Your Square Matrix
Input the values for your square matrix. Add or remove rows/columns as needed.
Trace of the Matrix:
Visualizing Diagonal Elements
Diagonal elements contributing to the trace are highlighted.
What is Matrix Trace?
In linear algebra, the trace of a square matrix is the sum of the elements on the main diagonal (from the upper left to the lower right).
For a square matrix $$A$$, the trace $$Tr(A)$$ is calculated as:
$$ Tr(A) = \sum_{i=1}^{n} a_{ii} $$
Where $$a_{ii}$$ are the diagonal elements of the matrix $$A$$.
The trace is only defined for square matrices. It has various applications in linear algebra, statistics, and other areas of mathematics.
Example
For the matrix:
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
The trace is 1 + 5 + 9 = 15.