Diagonalization of Symmetric Matrices
47 min 2 Examples
- Overview of Symmetric Matrices
- Theorem and Definitions for Diagonalization (Example #1 – Orthogonally Diagonalize)
- Diagonalization vs Orthogonal Diagonalization (Example #2 – Orthogonally Diagonalize with Gram-Schmidt)
- Spectral Theorem for Symmetric Matrices and Spectral Decomposition
Matrix of the Quadratic Form
59 min 9 Examples
- Overview of Quadratic Forms
- Compute the Quadratic Form given a matrix (Example #1)
- Find the Matrix of the Quadratic Form (Examples #2-3)
- Change of Variable in Quadratic Form and Principal Axes Theorem (Examples #4-5)
- Geometric View of the Principal Axis, Classifying Quadratic Forms, and Naming Conics (Examples #6-8)
- Classify Quadratic Form, Principal Axis, and Angle of Rotation (Example #9)
Chapter Test
43 min 6 Examples
- Find the matrix of the quadratic form (Problems #1a-c) and the quadratic form of the symmetric matrix (Problems #2a-c)
- Find the quadratic form of the symmetric matrix (Problems #2a-c)
- Determine if the matrix is orthogonal and find the inverse (Problem #3)
- Orthogonally diagonalize the matrix (Problem #4)
- Transform the given quadratic form and classify the new quadratic (Problem #5)
- True or False questions (Problems #6a-e)