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Linear algebra for advanced studies
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Module 4
Eigenvalues, Eigenvectors, and Diagonalization
1
Eigenvalues and Eigenvectors: Invariant Directions of Linear Transformations
Relate eigenvalues and eigenvectors to the geometric action of a linear transformation as invariant directions.
2
Eigenvalues and Eigenvectors: The Characteristic Polynomial
Compute the characteristic polynomial to find eigenvalues and their corresponding eigenvectors.
3
Algebraic vs. Geometric Multiplicity
Distinguish between the algebraic and geometric multiplicity of an eigenvalue.
4
Matrix Diagonalization Conditions
Determine the conditions under which a matrix is diagonalizable.
5
Diagonalizing a Matrix
Construct the diagonalization of a matrix, if it exists.
6
Matrix Powers Through Diagonalization
Apply diagonalization to efficiently compute powers of a matrix.
Previous module
Inner Products and Orthogonality
Next module
Spectral Theory for Symmetric & Hermitian Operators