(1.3 hours to learn)
Diagonalization refers to factorizing a matrix as A = SDS^-1, where D is a diagonal matrix. The entries of D correspond to the eigenvalues of A, and the columns of S correspond to the eigenvectors. The diagonal representation is useful for computing powers of matrices. Unfortunately, not all matrices are diagonalizable.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
Location: Section "Similarity and diagonalization"
- complex vectors and matrices
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 9.2, "Eigenvalues, eigenvectors, and applications," subsection 9.2.2, "Diagonalizability"
- linear transformations as matrices
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 6.2, "Diagonalizing a matrix"
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