Linked from

The 22 pages that link to Rank–nullity theorem, each with the reason it gives.

• Linear algebraRelated: It links the independent outputs of a map to the dimensions of its kernel and domain.

• Incidence matrixRelated: It relates incidence-matrix rank to the dimension of its null space.

• Dual spaceRelated: Dual maps preserve rank in finite dimensions, linking the constraints they impose to the original map.

• Linear mapRelated: It links the dimension of the image to the size of the kernel.

• System of linear equationsRelated: Rank and nullity determine whether solutions are unique and how many free variables remain.

• Invertible matrixRelated: For a square invertible matrix, full rank forces nullity zero.

• Surjective functionRelated: It turns surjectivity of finite-dimensional linear maps into a dimension condition.

• Image (mathematics)Related: The theorem measures the image through the rank of a linear map.

• Inverse function theoremRelated: It clarifies why an injective square derivative is also invertible.

• Kernel (linear algebra)Related: It quantifies the tradeoff between outputs retained and dimensions collapsed into the kernel.

• Rank (linear algebra)Related: It converts rank into the dimension of the solution space of the associated homogeneous system.

• Ordinary least squaresRelated: The design matrix's rank determines whether OLS coefficients are uniquely identifiable.

• Fredholm alternativeRelated: It gives the finite-dimensional dimension balance underlying the solvability alternative.

• Finite-dimensional vector spaceRelated: It divides the domain's dimensions between mapped directions and directions sent to zero.

• Fundamental theorem of linear algebraRelated: It supplies the dimension balance underlying the theorem’s four subspaces.

• Siegel's lemmaRelated: A sufficiently large variable space leaves a nontrivial rational kernel to search for integer points in.

• Buckingham π theoremRelated: It explains why the number of independent groups is n minus the dimension-matrix rank.

• Dimension theorem for vector spacesRelated: Rank and nullity are the image and kernel dimensions in this dimension formula.

• Rouché–Capelli theoremRelated: It explains why the number of free variables is the number of unknowns minus the coefficient matrix’s rank.

• Steinitz exchange lemmaRelated: Both results connect counts of independent directions to finite-dimensional structure.