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Mathematics

Linear Transformations and Their Geometric Interpretations

Quick fact

A linear transformation is completely determined by what it does to the basis vectors—just knowing where the unit vectors go tells you where every vector goes. This is why a matrix captures the transformation in a compact grid of numbers.

Why this is interesting

Imagine stretching, rotating, or squishing a photo on your phone—these are linear transformations. But what makes a transformation 'linear', and why do they always keep straight lines straight?

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Linear Transformations and Their Geometric Interpretations

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