Math Problem Statement
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Quadratic Forms
Orthogonal Transformation
Eigenvalues and Eigenvectors
Formulas
Q = x^T A x
A = orthogonal P^T D P, where D is diagonal
Eigenvalues of A give the canonical form
Theorems
Orthogonal Diagonalization Theorem
Rank-Nullity Theorem
Sylvester's Law of Inertia
Suitable Grade Level
Undergraduate (Linear Algebra Course)
Related Recommendation
Orthogonal Reduction of a Quadratic Form and Finding Rank, Index, Signature, and Nature
Diagonalizing a Quadratic Form and Finding its Rank using Orthogonal Transformation
Canonical Form of a Quadratic Form: 2x² + 2y² + 2z² - 2xy + 2xz - 2yz
Reducing a Quadratic Form to Canonical Signature via Diagonalization
Reduction of Quadratic Form 2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2xz to Canonical Form Using Orthogonal Transformation