Diagonalization

Fourier transform diagonalization

Fourier transform diagonalization
  1. What is the diagonalization formula?
  2. How does diagonalization work?
  3. Where is diagonalization used?

What is the diagonalization formula?

Diagonalization Proof

Cei = vi, and hence ei = C-1vi. To obtain the columns of D, we multiply by the standard coordinate vectors.

How does diagonalization work?

Diagonalizing means to find a basis which turns this representation in diagonal form. The matrix P represents an operator which changes your basis, and multiplying those matrices as written corresponds to changing basis, applying the operator, and changing back to the original basis so that nobody gets hurt.

Where is diagonalization used?

Matrix diagonalization is useful in many computations involving matrices, because multiplying diagonal matrices is quite simple compared to multiplying arbitrary square matrices.

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