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EdU/Linear algebra

Transformation
in an eigenvector basis

A =PDP−1
  1. P−1
    1.

    Converts v from the standard basis into B-basis coordinates.

  2. D
    2.

    Scales the vector's components along the B-basis directions.

  3. P
    3.

    Converts the resulting coordinates back into the standard basis.

1 / 3P⁻¹Start with v
xyb₁b₂vb₁2b₁−b₂−½b₂Av

Standard basis

v = (2, 0)

Here b₁ ⟂ b₂. D = diag(2, ½)

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