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  • Echelon matrices

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  • Example of putting a matrix in echelon form
  • Example of putting a matrix in echelon form and identifying the pivot columns
  • Definition of (echelon matrix/matrix in (row) echelon form)
  • Gauss-Jordan procedure to put a matrix into reduced row echelon form
  • Example of (echelon matrix/matrix in (row) echelon form)
  • Definition of (row) echelon form of a matrix
  • Definition of matrix in reduced row echelon form
  • Definition of reduced row echelon form of a matrix
  • Definition of row reduce a matrix
  • Example of row reducing a 3-by-3 matrix
  • Example of row reducing a 4-by-4 matrix
  • Every matrix is row-equivalent to a matrix in reduced row echelon form.
  • Every matrix is row-equivalent to only one matrix in reduced row echelon form.
  • Definition of extended reduced row echelon form of a matrix
  • Theorem describing properties of the block matrices of the extended reduced row echelon form of a matrix
  • Theorem describing spaces associated to the block matrices of the extended reduced row echelon form of a matrix
  • Theorem describing the dimension of spaces associated to the block matrices of the extended reduced row echelon form of a matrix
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  1. Theorem describing the dimension of spaces associated to the block matrices of the extended reduced row echelon form of a matrix

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  • Definition of distance between vectors#24091
  • Definition of domain of a linear transformation#23840
  • Definition of echelon form of a linear system#23422
  • Definition of (echelon matrix/matrix in (row) echelon form)#23539
  • Definition of eigenspace of a linear transformation#24050
  • Definition of eigenspace of a matrix#23684
  • Definition of eigenvalue/characteristic value of a linear transformation#24042
  • Definition of eigenvalue of a matrix#23681
  • Definition of eigenvector/characteristic vector of a linear transformation#24043
  • Definition of eigenvector of a matrix#23682
  • Definition of elementary matrix#23557
  • Definition of entry/component of a vector#23783
  • Definition of equality of matrices#23459
  • Definition of equality of vectors#23785
  • Definition of equation operations on a linear system#23424
  • Definition of equivalent matrices#23604
  • Definition of equivalent systems of linear equations#23426
  • Definition of extended reduced row echelon form of a matrix#23550
  • Definition of free/independent variable in a linear system#23443
  • Definition of generalized inverse of a matrix#23534
  • Definition of generalized kernel/null space of linear transformation#24060
  • Definition of generalized range space of a linear transformation#24039
  • Definition of geometric multiplicity of an eigenvalue#23697
  • Definition of Gram-Schmidt process#24093
  • Definition of Hermitian/self-adjoint matrix#23597
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