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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 |
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