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Key Concepts
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1. Elementary Operations
- Interchange of any two rows/columns.
- Multiplication of elements of any row/column by a non-zero scalar.
- Addition to elements of a row/column, corresponding elements of another row/column multiplied by k.
2. Trace of a Matrix
The sum of the diagonal elements of a square matrix. Tr(A+B) = Tr(A) + Tr(B).
3. Orthogonal Matrix
A matrix A is orthogonal if AAᵀ = I.