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- Fundamental_theorem_of_linear_algebra abstract "In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. These may be stated concretely in terms of the rank r of an m × n matrix A and its singular value decomposition:First, each matrix (has rows and columns) induces four fundamental subspaces. These fundamental subspaces are:Secondly: In , , that is, the nullspace is the orthogonal complement of the row space In , , that is, the left nullspace is the orthogonal complement of the column space.The dimensions of the subspaces are related by the rank–nullity theorem, and follow from the above theorem.Further, all these spaces are intrinsically defined – they do not require a choice of basis – in which case one rewrites this in terms of abstract vector spaces, operators, and the dual spaces as and the kernel and image of are the cokernel and coimage of .".
- Fundamental_theorem_of_linear_algebra thumbnail The_four_subspaces.svg?width=300.
- Fundamental_theorem_of_linear_algebra wikiPageExternalLink lecture10.htm.
- Fundamental_theorem_of_linear_algebra wikiPageExternalLink strangpaper.pdf.
- Fundamental_theorem_of_linear_algebra wikiPageID "1048334".
- Fundamental_theorem_of_linear_algebra wikiPageRevisionID "575009607".
- Fundamental_theorem_of_linear_algebra hasPhotoCollection Fundamental_theorem_of_linear_algebra.
- Fundamental_theorem_of_linear_algebra subject Category:Fundamental_theorems.
- Fundamental_theorem_of_linear_algebra subject Category:Isomorphism_theorems.
- Fundamental_theorem_of_linear_algebra subject Category:Theorems_in_linear_algebra.
- Fundamental_theorem_of_linear_algebra type Abstraction100002137.
- Fundamental_theorem_of_linear_algebra type Communication100033020.
- Fundamental_theorem_of_linear_algebra type FundamentalTheorems.
- Fundamental_theorem_of_linear_algebra type IsomorphismTheorems.
- Fundamental_theorem_of_linear_algebra type Message106598915.
- Fundamental_theorem_of_linear_algebra type Proposition106750804.
- Fundamental_theorem_of_linear_algebra type Statement106722453.
- Fundamental_theorem_of_linear_algebra type Theorem106752293.
- Fundamental_theorem_of_linear_algebra type TheoremsInLinearAlgebra.
- Fundamental_theorem_of_linear_algebra comment "In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. These may be stated concretely in terms of the rank r of an m × n matrix A and its singular value decomposition:First, each matrix (has rows and columns) induces four fundamental subspaces.".
- Fundamental_theorem_of_linear_algebra label "Fundamental theorem of linear algebra".
- Fundamental_theorem_of_linear_algebra label "線型代数学の基本定理".
- Fundamental_theorem_of_linear_algebra label "线性代数基本定理".
- Fundamental_theorem_of_linear_algebra sameAs 線型代数学の基本定理.
- Fundamental_theorem_of_linear_algebra sameAs m.041g9b.
- Fundamental_theorem_of_linear_algebra sameAs Q5508975.
- Fundamental_theorem_of_linear_algebra sameAs Q5508975.
- Fundamental_theorem_of_linear_algebra sameAs Fundamental_theorem_of_linear_algebra.
- Fundamental_theorem_of_linear_algebra wasDerivedFrom Fundamental_theorem_of_linear_algebra?oldid=575009607.
- Fundamental_theorem_of_linear_algebra depiction The_four_subspaces.svg.
- Fundamental_theorem_of_linear_algebra isPrimaryTopicOf Fundamental_theorem_of_linear_algebra.
