LaTeX
A\mathbf v=\lambda\mathbf vVariables
- A: square matrix
- v: nonzero eigenvector
- λ: eigenvalue
How to use this formula
Defines an eigenvector and its eigenvalue.
Important notes
- Solve det(A−λI)=0 for eigenvalues.
Quick example
A scales v without changing its direction.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Solve det(A−λI)=0 for eigenvalues.
- Preserve matrix order and verify dimension compatibility; multiplication and inversion are not generally commutative or always defined.
- Matrix and vector dimensions must be compatible, and any required inverse, determinant, rank, or basis condition must hold.
Worked example
A scales v without changing its direction.
Common mistakes
- Before substituting values into Eigenvalue Equation, 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 Eigenvalue Equation 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
A\mathbf v=\lambda\mathbf v. - 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 Eigenvalue Equation used for?
Defines an eigenvector and its eigenvalue.
Can I copy this formula as LaTeX?
Yes. Copy A\mathbf v=\lambda\mathbf v 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.