Linked from

The 14 pages that link to Eigenvector, each with the reason it gives.

• EigenvalueRelated: Its direction stays fixed while the eigenvalue gives its scaling factor.

• Principal component analysisRelated: Eigenvectors of the covariance matrix set the directions of PCA's components.

• Fixed pointCompared with: An eigenvector's direction is preserved; it is fixed only when its eigenvalue is one.

• Invariant subspaceBroader topic: Its one-dimensional span is an invariant subspace.

• Kernel (linear algebra)Compared with: Kernel vectors are mapped to zero, while eigenvectors with nonzero eigenvalues retain their direction.

• Scalar multiplicationBroader topic: Eigenvectors are characterized by scaling under a particular transformation.

• Square matrixRelated: Eigenvectors identify directions on which the matrix acts by simple scalar multiplication.

• Eigenvalue problemBroader topic: Finite-dimensional problems seek vectors satisfying the operator equation.

• Spectral theoremBroader topic: The theorem assembles eigenvectors into an orthonormal basis.

• Degenerate energy levelsNarrower topic: Quantum energy eigenstates are eigenvectors of the Hamiltonian.

• Spectral graph theoryNarrower topic: Graph eigenvectors can expose vertex groupings and influential locations.

• Chasles' theoremRelated: The rotation matrix's eigenvector with eigenvalue one points along its invariant axis.

• Perron–Frobenius theoremNarrower topic: Its special eigenvector also has every coordinate strictly positive.

• Gershgorin circle theoremRelated: Choosing its largest-magnitude coordinate yields the row inequality behind the disk bound.