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  • Linear systems of equations

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  • Basic terminology
  • Parametric form of the solution set of a system of linear equations
  • Parametric vector form of the solution set of a system of linear equations
  • Gaussian elimination as a method to solve a linear system
  • Definition of echelon form of a linear system
  • All echelon forms of a linear system have the same free variables
  • Definition of equation operations on a linear system
  • Equation operations on a linear system give an equivalent system.
  • Definition of equivalent systems of linear equations
  • The geometry of linear systems
  • Definition of consistent linear system
  • Definition of inconsistent linear system
  • Definition of homogeneous linear system of equations
  • Homogeneous linear systems are consistent.
  • Definition of nontrivial solution to a homogeneous linear system of equations
  • Definition of trivial solution to a homogeneous linear system of equations
  • A homogeneous system has a nontrivial solution if and only if it has a free variable.
  • The number of solutions to a linear system
  • Definition of basic/dependent/leading variable in a linear system
  • Definition of free/independent variable in a linear system
  • Theorem describing the vector form of sulutions to a linear system.
  • The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.
  • Definition of ill-conditioned linear system
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  1. The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.

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101–125 of 715 nodes
  • Definition of 0 matrix#23458
  • Definition of 0/trivial subspace#23964
  • Definition of 0 vector#23784
  • Definition of adjoint (conjugate transpose)#23506
  • Definition of adjugate/classical adjoint of a matrix#23748
  • Definition of (algebraic) multiplicity of an eigenvalue#23696
  • Definition of a lower triangular matrix#23563
  • Definition of angle between vectors#23915
  • Definition of an upper triangular matrix#23562
  • Definition of applying a polynomial to a linear transformation#24048
  • Definition of applying a polynomial to a square matrix#23700
  • Definition of augmented matrix (of a linear system)#23755
  • Definition of automorphism of a vector space#24007
  • Definition of a vector being orthogonal to a subspace#23919
  • Definition of band matrix#23593
  • Definition of basic/dependent/leading variable in a linear system#23442
  • Definition of basis of a vector space (or subspace)#23829
  • Definition of block diagonal matrix#23570
  • Definition of block/partitioned matrix#23568
  • Definition of change of coordinates matrix between two bases#23995
  • Definition of change-of-coordinates matrix relative to a given basis of R^n (or C^n)#23832
  • Definition of characteristic equation of a matrix#23702
  • Definition of characteristic polynomial of a linear transformation#24044
  • Definition of characteristic polynomial of a matrix#23701
  • Definition of Cholesky decomposition#23629
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1–2 of 2 public trees
  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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