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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 leading entry in a row of a matrix#23481
  • Definition of least-squares error of a linear system#23947
  • Definition of least-squares solution to a linear system#23946
  • Definition of left inverse of a matrix#23515
  • Definition of length/norm of a vector#24090
  • Definition of linear combination of vectors#23800
  • Definition of linear dependence relation on a set of vectors#23816
  • Definition of linear equation#23413
  • Definition of linearly dependent set of vectors: one of the vectors can be written as a linear combination of the other vectors#23821
  • Definition of linearly independent set of vectors: if a linear combination is 0#23819
  • Definition of linear transformation/homomorphism#24013
  • Definition of LU decomposition#23625
  • Definition of Markov matrix#23595
  • Definition of matrix#23449
  • Definition of matrix diagonalization#23610
  • Definition of matrix equation#23764
  • Definition of matrix in reduced row echelon form#23543
  • Definition of matrix multiplication#23489
  • Definition of matrix multiplication in terms of column vectors#23488
  • Definition of matrix null space (left)#23874
  • Definition of matrix null space (right)#23873
  • Definition of matrix representation of a linear system#23759
  • Definition of matrix representation of a linear transformation#23861
  • Definition of matrix representation of a linear transformation from a vector space to itself#24070
  • Definition of matrix representation of a linear transformation with respect to bases of the spaces#24068
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