Linear Algebra
Intermediate

Matrix Trace

Sum of the diagonal entries of a square matrix.

Formula

tr(A)=∑iaii\text{tr}(A) = \sum_i a_{ii}

Variables

a_{ii}Diagonal entries

Example

tr of I₃ = 3

Did You Know?

The trace of a matrix equals the sum of its eigenvalues, a fact that survives any change of coordinates.

matrix