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UNIT 2 LINEAR TRANSFORMATION AND DIAGONALIZATION
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A linear transformation is a rule that takes a vector and changes it (like stretching, rotating, or flipping) while keeping basic properties like addition and scaling intact; the null vector (or zero vector) is a special vector with all components equal to zero, representing no movement and always remaining unchanged under any linear transformation; and diagonalization is a method of simplifying a matrix by converting it into a diagonal form (with nonzero values only on the main diagonal), which makes calculations easier and helps understand how the transformation behaves.
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