Change of Basis Visualization

Math Visualization List

Change of Basis

The columns of matrix P represent the positions of the "new basis vectors" in the standard coordinate system.

New Basis Matrix P (Language Translator)

Vector coordinates in standard basis [x, y, z]

[2.0, 2.0, 2.0]

Vector coordinates in new basis [x', y', z']

[?, ?, ?]

A' = P⁻¹ A P

Meaning of Similar Matrices:
1. P: "Translate" new language coordinates into standard language.
2. A: Perform linear transformation in standard language.
3. P⁻¹: "Translate" the result back to new language.
Final Effect: The same transformation is completed in your new coordinate system.