Vector Spaces
- Introduction
- Creation of Vector Spaces and Arithmetic with Vectors
- Construction of a Vector Space
VectorSpace(K, n): Fld, RngIntElt → ModTupFldKSpace(K, n): Fld, RngIntElt → ModTupFldKModule(K, n): Fld, RngIntElt → ModFldKMatrixSpace(K, m, n): Fld, RngIntElt, RngIntElt → ModMatFldHom(V, W): ModTupFld, ModTupFld → ModMatFldExample: Create Q6Example: Create K35
- Construction of a Vector Space with Inner Product Matrix
- Construction of a Vector
- Deconstruction of a Vector
- Arithmetic with Vectors
u + v: ModTupFldElt, ModTupFldElt → ModTupFldElt- u: ModTupFldElt → ModTupFldEltu - v: ModTupFldElt, ModTupFldElt → ModTupFldEltx * u: FldElt, ModTupFldElt → ModTupFldEltu * x: ModTupFldElt, FldElt → ModTupFldEltu / x: ModTupFldElt, FldElt → ModTupFldEltNumberOfColumns(u): ModTupFldElt → RngIntEltNcols(u): ModTupFldElt → RngIntEltDepth(u): ModTupRngElt → RngIntElt(u, v): ModTupFldElt, ModTupFldElt → FldEltInnerProduct(u, v): ModTupFldElt, ModTupFldElt → FldEltIsZero(u): ModElt → BoolEltNorm(u): ModTupFldElt → FldEltNormalise(u): ModTupFldElt → ModTupFldEltNormalize(u): ModTupFldElt → ModTupFldEltRotate(u, k): ModTupFldElt, RngIntElt → ModTupFldEltRotate(~u, k): ModTupFldElt, RngIntEltNumberOfRows(u): ModTupFldElt → RngIntEltNrows(u): ModTupFldElt → RngIntEltSupport(u): ModTupFldElt → { RngElt }TensorProduct(u, v): ModTupFldElt, ModTupFldElt → FldEltTrace(u, F): ModTupFldElt, Fld → ModTupFldEltTrace(u): ModTupFldElt → ModTupFldEltWeight(u): ModTupFldElt → RngIntEltExample: ArithmeticExample: Inner Product
- Indexing Vectors and Matrices
u[i]: ModTupFldElt, RngIntElt → RngEltu[i]: ModTupFldElt, RngIntElt → ModTupFldEltu[i, j]: ModTupFldElt, RngIntElt, RngIntElt → ModTupFldEltu[i] := x: ModTupFldElt, RngIntElt, RngElt → ModTupFldEltu[i] := x: ModTupFldElt, RngIntElt, ModTupFldElt → ModTupFldEltu[i, j] := x: ModTupFldElt, RngIntElt, RngIntElt, ModTupFldElt → ModTupFldEltExample: Indexing
- Subspaces, Quotient Spaces and Homomorphisms
- Changing the Coefficient Field
ExtendField(V, L): ModTupFld, Fld → ModTupFld, MapHomRestrictField(V, L): ModTupFld, Fld → ModTupFld, MapHomVectorSpace(V, F): ModTupFld, Fld → ModTupFld, MapKSpace(V, F): ModTupFld, Fld → ModTupFld, MapKMatrixSpace(V, F): ModTupFld, Fld → ModTupFld, MapKModule(V, F): ModTupFld, Fld → ModTupFld, Map
- Basic Operations
- Reducing Vectors Relative to a Subspace
- Bases
- Operations with Linear Transformations
