QLinear is type safe library for linear algebra based on "macro-constructors"

• matrix

  [matrix| a b ; c d |] builds matrix 2x2 [ [a, b], [c, d] ]

  Example:

  [matrix| 1 2; 3 4 |] ~+~ [matrix| 2 3; 4 5 |] == [matrix| 3 5; 7 9 |] 

  Also you can't, for example, add two matrix with different size.

  [matrix| 1 2; 3 4 |] ~+~ [matrix| 1 2 3; 4 5 6; 7 8 9 |] -- will not be compiled

• vector

  [vector| a b c d |] builds matrix 4x1 [ [a], [b], [c], [d] ]

• operator

  [operator| (x, y) => (y, x) |] builds matrix 2x2 of operator [ [0, 1], [1, 0] ] that swaps coodrinates
  [operator| (x, y) => (2 * x, y) |] builds matrix 2x2 of operator [ [2, 0], [0, 1] ] that doubles x coordinate

  Example:

  [operator| (x, y) => (3 * y, x / 2) |] ~*~ [vector| 2 8 |] == [vector| 24 1 |]

• matrix: val11 val12 .. val1n; val21 val22 .. val2n; ..; valm1 valm2 .. valmn
• vector: val1 val2 .. valn
• operator: (var1, var2, .., varn) => (exp1, exp2, .., expn)
  where
  • val is number literal, variable or any Haskell expression between ( and )
  • var is Haskell variable
  • exp is any Haskell expression

Also there are basic operations as determinant, transposition, etc.