add
, SUBT
and MULT
), ALGB
provides:
STUDMULT
: (MATR
directory)
student multiplication of matrices (term by term)
TR
: trace of a matrix
TRAN
: transposed of a matrix (true transposed, no conjugation)
XY
: scalar produc of two vectors
cross
(MATR
directory): cross product of two 3-d vectors.
rref
: row reduction to echelon form. At level 2, the list
of pivoting coefficients is given, this is usefull to treat particular
cases.
MAD
: given a square matrix, returns
determinant, formal inverse, a list polynomial (see section 10.1)
and the characteristic polynomial.
idn
: to build a symbolic identity matrix
LU2
: given a square matrix, returns L-1 and U s.t.
A=LU (i.e. A=stk2
stk1
) where L and U
are lower and upper triangular
(maybe w.r.t. to a premutation matrix, this means that computing
the inverse of L or U is trivial). For comparison, the built-in
LU
returns three matrices L, U and P s.t. A=PLU.
DIAG
(MATR
directory): diagonalisation of a square
matrix (see 10.1)
RED
(MATR
directory)
DET
(MATR
directory): determinant (using the stupid
algorithm)
PCAR
(MATR
directory):
characteristic polynomial using DET