Linear Algebra: Eigenvalues and Eigenvectors
Collapse
All Linear AlgebraSolving Systems of Linear EquationsMatrix OperationsMatrix Inverses and Elementary MatricesDeterminants and Cramers RuleVector Operations and Linear CombinationsSpan and Linear IndependenceSubspaces Basis and DimensionRank and NullityChange of Basis and CoordinatesMatrix Transformations and Linear MapsEigenvalues and EigenvectorsDiagonalizationOrthogonality and ProjectionsLeast Squares Problems
AllNeeds AttentionEasyMediumHardVideo
Using a 2x2 matrix, identify eigenvectors and eigenvalues. Explain the transformation effects on vectors when multiplied with this matrix, including stretching, shrinking, and rotation dynamics. Consider cases with real and non-real eigenvalues and describe their implications for vector transformations.