LaTeX
q(x)=x^TAxVariables
- x: column vector
- A: square matrix
- q(x): scalar value
How to use this formula
Defines a scalar quadratic expression associated with a square matrix.
Important notes
- Only the symmetric part of A affects q(x).
- Positive definiteness is central in optimization and stability.
Quick example
For A=I, q(x)=||x||².
Applicability, worked calculation, and verification
Assumptions and domain checks
- Only the symmetric part of A affects q(x).
- Matrix and vector dimensions must be compatible, and any required inverse, determinant, rank, or basis condition must hold.
Worked example
For A=I, q(x)=||x||².
Common mistakes
- Before substituting values into Quadratic Form, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Do not assume commutativity, invertibility, independence, or full rank unless the required condition has been established.
Continue the workflow
Use Quadratic Form in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
q(x)=x^TAx. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Quadratic Form used for?
Defines a scalar quadratic expression associated with a square matrix.
Can I copy this formula as LaTeX?
Yes. Copy q(x)=x^TAx or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.