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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. Example of putting a matrix in echelon form and identifying the pivot columns

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  • Triangular matrices#23561
  • Two matrices of the same size are equivalent if and only if they have the same rank.#23607
  • Two vectors are orthogonal if and only if the Pythagorean Theorem holds.#23918
  • Unitary matrices#23587
  • Unitary matrices are invertible.#23589
  • Unitary matrices have orthogonal (orthonormal) rows/columns.#23590
  • Unitary matrices preserve inner products.#23591
  • Unitary matrices preserve orthogonal (orthonormal) bases.#23592
  • Using matrices to solve linear systems#23760
  • Vector space isomorphism is an equivalence relation.#24003
  • Vector spaces#23775
  • Vector spaces with the same dimension are isomprphic.#24005
  • Vector sum/addition interpreted geometrically in R^n (or C^n)#23797
  • Vector sum/addition is commutative and associative#23787
  • Visualise a linear transformation on R^2 by looking at the image of a region#23852
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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