Dashboard

Featured nodes

Roots

  • Public root

Templates

  • Guanyu's Latex template
  • Router template

Trees

  • Public trees
Related nodes

Parents1

  • Linear systems of equations

Siblings23
  • Sort by title
  • Sort by date

  • 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
KnowenBeta
#
  • Explore
  • Sign in
  1. The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.

Navigate

Jump to a node in this tree, or explore your trees and public knowledge.

Quick Navigation

Jump to a node or explore another tree.

  • Current tree nodes
  • Public trees
301–325 of 715 nodes
  • Definition of sum of subspaces#23968
  • Definition of symmetric matrix#23572
  • Definition of system of linear equations#23416
  • Definition of the 0/trivial subspace#23814
  • Definition of the determinant in terms of the effect of elementary row operations#23726
  • Definition of the imaginary part of a vector in C^n#23790
  • Definition of the least-squares linear fit to 2-dimensional data#23951
  • Definition of the (main) diagonal of a matrix#23455
  • Definition of the real part of a vector in C^n#23789
  • Definition of the standard basis of the m by n matrices#23834
  • Definition of the standard basis of the polynomials of degree at most n#23833
  • Definition of the standard matrix for a linear transformation#23857
  • Definition of the standard/natural basis of R^n (or C^n)#23830
  • Definition of trace of a matrix#23715
  • Definition of transpose of a matrix#23503
  • Definition of trivial linear dependence relation on a set of vectors#23817
  • Definition of trivial solution to a homogeneous linear system of equations#23436
  • Definition of unitary matrix#23588
  • Definition of unit matrix#23554
  • Definition of unit vector#23909
  • Definition of Vandermonde matrix#23594
  • Definition of vector#23779
  • Definition of vector addition#23955
  • Definition of vector-scalar multiplication#23792
  • Definition of vector sum/addition#23786
« First ← Previous ... 9 10 11 12 13 14 15 16 17 ... Next → Last »
1–2 of 2 public trees
  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

Knowen© 2026 KTree Inc.

ExplorePricingIntegrationsContact usLeave feedback