The trace of a square matrix is the sum of the elements on its main diagonal (the diagonal from the top left to the bottom right).

Formula:

For an \(n \times n\) matrix A, the trace, denoted as \(\text{tr}(A)\), is:

\(\text{tr}(A) = \sum_{i=1}^{n} A_{ii} = A_{11} + A_{22} + \dots + A_{nn}\)

Properties:

• The trace is only defined for square matrices.
• \(\text{tr}(A+B) = \text{tr}(A) + \text{tr}(B)\)
• \(\text{tr}(cA) = c \cdot \text{tr}(A)\)