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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 matrix-scalar multiplication#23471
  • Definition of matrix-vector product#23483
  • Definition of m by n matrix#23452
  • Definition of minimal polynomial of a linear transformation#24045
  • Definition of minimal polynomial of a matrix#23703
  • Definition of multilinear function#23733
  • Definition of nilpotent linear transformation#23860
  • Definition of nilpotent matrix#23581
  • Definition of nonsingular matrix: matrix is invertible#23641
  • Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solution#23642
  • Definition of nontrivial solution to a homogeneous linear system of equations#23435
  • Definition of normal matrix#23600
  • Definition of norm/length of a vector#23908
  • Definition of (not necessarily orthogonal) projection onto a component of a direct sum#23940
  • Definition of nullity of a linear transformation#23884
  • Definition of nullity of a matrix#23675
  • Definition of one-to-one/injective linear transformation#23845
  • Definition of onto/surjective linear transformation#23844
  • Definition of orthogonal basis of a (sub)space#23928
  • Definition of orthogonal complement of a subspace#23920
  • Definition of orthogonally diagonalizable matrix#23577
  • Definition of orthogonal matrix#23586
  • Definition of (orthogonal) projection of one vector onto another vector#23938
  • Definition of (orthogonal) projection onto a subspace#23941
  • Definition of orthogonal set of vectors#23925
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  • Aspen Summer 2016 - Entanglement Matters#1213
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