MatrixManipulationTable

Those words that manipulate matrix and vector objects.

• Matrices= A, B, M, N, R, Z(complex) ; Vectors= V, W, U
• Note also dimensions! Row= R, r, m, i ; Column= C, c, n, j

  CATALOG NAME	ARGUMENTS	RESULT
  *	[B]r ·C | [A] | z, [A]R·c | z | [A]	[M]r ·c | [M] | [M] @ R≡C
  +	[A]R·C, [B]R·C	[M]R·C
  -	[A]R·C, [B]R·C	[M]R·C
  /	[B]R·c | [A], [sys]C·C | z	[solved]R·c | [M] @ R≡C
  ABS	[A]	|A|
  ARRY→	[M] | [V]	elem..., {r c} | {n}
  AUGMENT	[A]r ·C, [V]C | [A]k·C [V]C, elem | [V]C	[A](r+1) ·C | [A](r+k) ·C [V]C+1 | [A]2·C
  AXL	[A] | { }	{ } | [A]
  AXM	[A]sym | [M]num	[M]num | [A]sym
  AXQ	[Quad]n·n, [var]n	'Quad', [var]n
  BASIS	{ [Vspace]...}	{ [Vbasis]...}
  CHOLESKY	[M]n·n	[UpperTriangular]n·n
  CNRM	[A]	ColumnNorm
  COL+	[A] | [A] | [V], [B] | [V] | elem, p	[M] | [M] | [W]
  COL-	[A] | [V], pos	[M] | [W], [W] |elem
  COL→	[V]...| elem..., n	[A] | [V]
  CON	{n} | {r c} | [A], z	[V] | [M] | [M] @ elems≡z
  COND	[M]n·n	ConditionNumber
  CONJ	[Z]	[Z]conjugate
  CROSS	[V]2| 3, [W]2| 3	[U]n=3
  CSWP	[A] | [V], col1, col2	[M] | [W]
  CYLIN	@ -15 CF -16 SF	@ R<)Z
  C→R	[Z]	[X], [Y]
  DET	[M]n·n	Determinant
  DIAGMAP	[A]n·n, «→ M «...» »	[N]n·n
  DIAG→	[diag], {n} | {r c}	[M]n·n | [M]r·c
  DOT	[A]n, [B]n	DotProduct
  EGV	[M]n·n	[N]Eigenvec, [V]Eigenval
  EGVL	[M]n·n	[V]Eigenvalues
  FFT	[V]p | [A]p·q	[W]p | [M]p·q @ p, q = 2^n
  GAUSS	'QuadraticForm', [var...]	[diag], [[ChangeofBase]], 'SumofSquares', [var...]
  GET	[A], {r c}| p | [V], {p}| p	elemrc | elemp | elemp | elemp
  GETI	[A], {r c}| p | [V], {p}| p	[A], {r c}++| p++, elmrc|elmp | [V], {p}++| p++, elmp|elmp
  GRAMSCHMIDT	[VectorSpaceBase], «→ P Q« scalar* »»	[OrthonormalBase]
  HADAMARD	[A]R·C, [B]R·C	[elemAij·elemBij,...]R·C
  HILBERT	size	[HilbertMatrix]
  IBASIS	{ [Vspace]...}A, { [Vspace]...}B	{ [baseIsect]...}
  IDN	n. | n | [M]n·n	[ I ]Num | [ I ]Symb | [ I ]Symb
  IFFT	[V]p | [A]p·q	[W]p | [M]p·q @ p, q = 2^n
  IM	[Z] | [R]	[R]IM | [R]zero
  IMAGE	[Basis]n·n	{ [Vbasis]...}
  INV	[M]n·n	[N]n·n
  ISOM	[Isometry]n·n @ n=2|3	{ [char elems] | <), +|-1}
  JORDAN	[A]n·n	'PMin', 'PChar', {Char:[V] Eigen:[W] ...}, [Eval]n
  KER	[Basis]n·n	{ [Vkernel]...}
  LCXM	n, m, « → i j «...» »	[M]n·m
  LINSOLVE	['lin' 'sys' 'eq']n, [var]n	{ 'varn=result',...}
  LQ	[A]n·m	[LowerTrapetz]m·n, [Qortho]m·n, [Perm]m·m
  LSQ	[V]R | [B]c·R, [A]R·R	[W]R | [M]c·R
  LU	[A]n·n	[LowerTriang], [UpperTriang], [Perm]
  MAD	[A]n·n	det, [A]inv, { [coef]n·n...}, 'PolyChar'
  MAP	[el...], «...»	[prog(el)...]
  MATR	@ 69 83 MENUXY	@ TRAN|HADAM|rref|REF|AXM|AXL
  MKISOM	{ | [char elems], <) | }, +|-1	[Isometry]n·n @ n=2|3
  NEG	[A]	[-A]
  OBJ→	[M] | [V]	elem..., {r c} | {n}
  PCAR	[A]n·n	'PolyChar'
  PMINI	[A]n·n	[PolyMin]n·n @ 1st r≠0
  PUT	[M], {r c}| p, elem | [V], {p}| p, elem	[N] | [W]
  PUTI	[M], {r c}| p, elem | [V], {p}| p, elem	[N], {r c}++| p++ | [W], {p}++| p++
  QR	[M]n·m	[Qortho]m·m, [RupTraptz]m·n, [Perm]n·n
  qr	[M]n·n	[Qortho]n·n, [Rtriang]n·n
  QXA	'Quad', [vars]	[M]n·n [vars]
  RANK	[M]n·n	Rank
  RANM	[M] |{r c}| [V] |{n}	[Mrandom] | [Vrandom]
  RATIO	[B]R·c | [A], [sys]C·C | z	[solved]R·c | [M] @ R≡C
  RCI	[M] | [V], factor, r|p	[N] | [W]
  RCIJ	[M] | [V], factor, r1|p1, r2|p2	[N] | [W]
  RDM	[M] | [V], {r c} [M] | [V], {n}	[M]r·c [V]n
  RE	[Z]	[Re]
  RECT	@ -15 CF -16 CF	@ XYZ
  REF	[Msys]n·(n+1)	[Aresult]n·(n+1)
  REPL	[A], {r c}, [B] [V], {n}, [W]	[M] [U]
  RND	[A], digits	[A]rounded
  RNRM	[A]	RowNorm
  ROW+	[A] | [A] | [V], [B] | [V] | elem, p	[M] | [M] | [W]
  ROW-	[A] | [V], pos	[M] | [W], [W] |elem
  ROW→	[V]...| elem..., n	[A] | [V]
  RREF	[Msys]n·(n+1)	[Aresult]n·(n+1)
  rref	[Msys]n·(n+1)	Pivots:{...}, [Aresult]n·(n+1)
  RREFMOD	[Msys]n·(n+1)	[Aresult]n·(n+1) @ MODULO
  RSD	[B]rA·c,[A]rB·cZr,[Z]rAc·c [V]n, [A]rVn·cWn, [W]n	[M]B−A·Z [U]V−A·W
  RSWP	[A] | [V], row1, row2	[M] | [W]
  R→C	[Re]R·C, [Im]R·C	[Z]R·C
  SCHUR	[A] | [Z]	[Qortho], [upperquasiTriang] | [Qunitary], [upperTriang]
  SIZE	[M]r·c | [V]n	{ r c } | n
  SNRM	[A] | [V]	SpectralNorm
  SPHERE	@ -15 SF -16 SF	@ R<)<)
  SQ	[M]n·n	[N]n·n
  SRAD	[M]n·n	SpectralRadius
  SUB	[M], p|{r c}, P|{r c} [V], p, P	[N] [W]
  SVD	[A]m·n	[Uortho]m·m, [Vortho]n·n, [S]min(m,n)
  SVL	[M]m·n	[SingularValues]min(m,n)
  SYLVESTER	[Quad]n·n	[diag]n, [Mchange]n·n
  SYST2MAT	['sys' 'lin' 'eq']n, [var]n	[M]n·(n+1)
  TRACE	[M]n·n	Trace
  TRAN	[A]	[C]
  TRN	[A]	[Conj]
  TRNC	[A], digits	[A]truncated
  VANDERMONDE	[elemn...elem1-][-c	[elemn^(r-1)..elem1^(r-1)-][-c·r @ c=r
  V→	[V]n	elemn,...,elem1
  →ARRY	elem..., n|{n}|{r c}	[A]
  →COL	[V] | [M]	elem...| [col]..., n
  →DIAG	[A]R·c	[diagonals]R
  →ROW	[V] | [M]	elem...| [row]..., n
  →V2	x,y | r,θ	[x y] | [r θ]
  →V3	x,y,z | r,θ,z | r,θ,φ	[x y z] | [r θ z] | [r θ φ]
  CATALOG NAME	ARGUMENTS	RESULT