Mathematics · University
Eigenvalue from a known eigenvector · formula reference
Verify the vector is nonzero. Distinct eigenvectors can have distinct eigenvalues.
Formula
Verify the vector is nonzero. Distinct eigenvectors can have distinct eigenvalues.
A(1,1)ᵀ = (a+b)(1,1)ᵀ for A=[[a,b],[b,a]]
Worked example
For A = [[13,9],[9,13]], find the eigenvalue belonging to v = (1,1). Round the final result to 4 decimal places if needed.
Multiplication gives Av = (22,22) = (22)v.
22
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.