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  • Matrix diagonalization

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  • Definition of matrix diagonalization
  • Definition of diagonalizable matrix
  • An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
  • An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.
  • An n-by-n matrix is diagonalizable if and only if the characteristic polynomial factors completely
  • A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.
  • An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).
  • An n-by-n matrix with n distinct eigenvalues is diagonalizable.
  • Formula for diagonalizing a real 2-by-2 matrix with a complex eigenvalue.
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  1. An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).

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  • Definition of row equivalent matrices#23479
  • Definition of row operations on a matrix#23475
  • Definition of row reduce a matrix#23545
  • Definition of row space of a matrix#23880
  • Definition of scalar#23778
  • Definition of scalar multiple of a linear transformation#24017
  • Definition of Schur triangulation#23633
  • Definition of similarity transform#23637
  • Definition of similar matrices#23635
  • Definition of singular matrix (not nonsingular)#23643
  • Definition of singular value decomposition (SVD)#23623
  • Definition of size of a matrix#23451
  • Definition of size of a vector#23782
  • Definition of skew-symmetric matrix#23579
  • Definition of solution set of a system of linear equations#23418
  • Definition of solution to a linear equation#23415
  • Definition of solution to a system of linear equations#23417
  • Definition of solution vector of a linear system#23758
  • Definition of spanning/generating set for a space or subspace#23978
  • Definition of span of a set of vectors#23805
  • Definition of square matrix#23454
  • Definition of subspace#23812
  • Definition of subspace spanned by a set of a set of vectors#23813
  • Definition of sum of linear transformations#24015
  • Definition of sum of matrices#23462
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