Subjects Linear Algebra

Matrix Trace Ff4239

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Matrix Trace Ff4239


1. The problem is to find the trace of a matrix.\n\n2. The trace of a square matrix is the sum of the elements on its main diagonal.\n\n3. If the matrix is \( A = \begin{bmatrix} a_{11} & a_{12} & \cdots \\ a_{21} & a_{22} & \cdots \\ \vdots & \vdots & \ddots \end{bmatrix} \), then the trace is given by \( \text{trace}(A) = \sum_{i} a_{ii} \).\n\n4. To find the trace, simply add the diagonal elements \( a_{11}, a_{22}, a_{33}, \ldots \).\n\n5. This operation is only defined for square matrices (same number of rows and columns).\n\n6. Example: For \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), the trace is \( 1 + 4 = 5 \).