Vectors and matrices

Comma separates columns, semicolon separates rows.

[1,2,3] // [1, 2, 3]
[1,2;3,4] // [1, 2; 3, 4]

Element-wise arithmetic

[1,2,3] * 10 // [10, 20, 30]
[1,2,3] + [10,20,30] // [11, 22, 33]

Matrix products

Multiplying two matrices whose shapes line up performs a real matrix product rather than an element-wise one.

[1, 2; 3, 4] * [1; 2] // [5; 11]

Indexing

Indices are zero-based.

[1,2,3][0] // 1
[1,2;3,4][1,1] // 4

Linear algebra

[1,2;3,4]^T // [1, 3; 2, 4]
det([1,2;3,4]) // -2
[1,2;3,4]^-1 // [-2.00, 1.00; 1.50, -0.50]

The inverse operator leaves ordinary numbers alone, so 5^-1 is still 0.2.

A matrix whose entries contain unknowns is inverted symbolically, and those entries carry exact rational coefficients rather than floating-point ones. That removes a class of wrong answer: a pivot that is structurally zero could previously arrive as a value like 0.0000000000000000555 after elimination and be treated as non-zero, so a singular matrix was reported as invertible. See Symbolic evaluation.