Linearly Independent Eigenvectors

Some articles on eigenvectors, linearly independent eigenvectors:

Defective Matrix
... that does not have a complete basis of eigenvectors, and is therefore not diagonalizable ... In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors ... A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations ...
Eigenvalues And Eigenvectors - Eigenvalues and Eigenvectors of Matrices - Algebraic and Geometric Multiplicities
... measuring, roughly speaking, the number of eigenvectors belonging to λi ... number of linearly independent eigenvectors with that eigenvalue ... The total number of linearly independent eigenvectors, Nx, is given by summing the geometric multiplicities Over a complex vector space, the sum of the algebraic multiplicities will equal the ...

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