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Linear transformation

Overview#

Linear transformation implies there must be no curves (only lines) and the origin must remain fixed.

Think of linear transformations as keeping gridlines parallel and evenly spaced.

Linear transformation is a Function (or Algorithm). So a linear Function is a Function that takes a vector input and outputs a vector.

Linear transformation implies there must be no curves (only lines) and the origin must remain fixed. Think of linear transformations as keeping gridlines parallel and evenly spaced.

Basis vectors define the coordinate system or origin. Commonly

  • iHat (x-axis)
  • jHat (y-axis)
  • kHat (z-axis)
are used.

Linear transformation requires that you perform matrix multiplication of the vector by the changes to the Basis vectors (iHat, jHat) Any Linear transformation can be described as iHat and jHat this is because any other vector could be described as a linear combination of those basis vectors a vector with coordinates x, y is x times iHat plus y times jHat

More Information#

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