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
126–150 of 715 nodes
  • Definition of codomain of a linear transformation#23841
  • Definition of coefficient matrix of a linear system#23756
  • Definition of coefficients of a linear equation#23414
  • Definition of cofactor/submatrix of a matrix#23717
  • Definition of column rank of a matrix#23673
  • Definition of column space of a matrix#23875
  • Definition of column vector#23780
  • Definition of complement of a subspace#23975
  • Definition of composition of linear transformations#24023
  • Definition of conjugate of a matrix#23465
  • Definition of conjugate of a vector in C^n#23788
  • Definition of consistent linear system#23431
  • Definition of constant vector of a linear system#23757
  • Definition of coordinates relative to a given basis#23835
  • Definition of coordinate vector/mapping/representation relative to a given basis#23991
  • Definition of cross product#24121
  • Definition of determinant of a matrix as a cofactor expansion across the first row#23718
  • Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.#23724
  • Definition of diagonalizable linear transformation#24041
  • Definition of diagonalizable matrix#23611
  • Definition of diagonal matrix#23456
  • Definition of dimension of a vector space (or subspace)#23837
  • Definition of dimension of a vector space (or subspace) being finite or infinite#24009
  • Definition of direct sum of subspaces#23970
  • Definition of distance#23911
« First ← Previous 1 2 3 4 5 6 7 8 9 10 ... Next → Last »
1–2 of 2 public trees
  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

Knowen© 2026 KTree Inc.

ExplorePricingIntegrationsContact usLeave feedback