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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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151–175 of 715 nodes
  • 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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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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