Linear algebra.

  In addition to the arithmetic usual operations on matrices and vectors (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

 
• Diagonalisation
• Reduction of matrices.
  • Solving a linear system.
  • Inversion
  • Determinant
• The 301 instruction.
• Other examples.
  • Stack input/output for 306