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  • Linear systems and echelon matrices

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  • The echelon form can be used to determine if a linear system is consistent.
  • Example of using the echelon form to determine if a linear system is consistent.
  • The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.
  • The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.
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  1. The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.

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  • Definition of matrix-scalar multiplication#23471
  • Definition of matrix-vector product#23483
  • Definition of m by n matrix#23452
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  • Definition of minimal polynomial of a matrix#23703
  • Definition of multilinear function#23733
  • Definition of nilpotent linear transformation#23860
  • Definition of nilpotent matrix#23581
  • Definition of nonsingular matrix: matrix is invertible#23641
  • Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solution#23642
  • Definition of nontrivial solution to a homogeneous linear system of equations#23435
  • Definition of normal matrix#23600
  • Definition of norm/length of a vector#23908
  • Definition of (not necessarily orthogonal) projection onto a component of a direct sum#23940
  • Definition of nullity of a linear transformation#23884
  • Definition of nullity of a matrix#23675
  • Definition of one-to-one/injective linear transformation#23845
  • Definition of onto/surjective linear transformation#23844
  • Definition of orthogonal basis of a (sub)space#23928
  • Definition of orthogonal complement of a subspace#23920
  • Definition of orthogonally diagonalizable matrix#23577
  • Definition of orthogonal matrix#23586
  • Definition of (orthogonal) projection of one vector onto another vector#23938
  • Definition of (orthogonal) projection onto a subspace#23941
  • Definition of orthogonal set of vectors#23925
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