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On this page
  • Matrix as Linear Transformation
  • Matrix as a Projection
  1. Linear Algebra

Matrix Interpretation

PreviousPositive (Semi)Definite MatricesNextDot Product as Linear Transformation and Duality of Vector-Linear Transformation

Last updated 11 months ago

Matrix as Linear Transformation

  • Any matrix-vector product is essentially a linear transformation.

  • Any linear transformation can be seen as a change of basis as well.

  • So matrix multiplication is basically a linear transformation of a vector or change of basis.

Matrix as a Projection

ATbA^TbATb where AAAis a matrix and bbbis a vector, denotes the projection of bbb on the columns space of AAA.

LogoTwo Forms of the Dot Product