Science & Data

Matrices

Build matrices of real numbers as literals, do matrix algebra, and call linear-algebra functions like determinant, inverse, and eigenvalues.

[1 2 3, 4 5 6]
[1 2, 3 4] * [5 6, 7 8]
determinant([1 2 3, 4 5 6, 7 8 10])
eigenvalues([2 1, 1 2])

Literals

Wrap entries in square brackets. Space separates columns; comma or semicolon separates rows. Entries are plain numbers (negatives and decimals are fine).

[1 2 3, 4 5 6, 7 8 9]
[1 2 3; 4 5 6]
[1.5 -2, 3 4]
[5]

[1 2 3] is a row vector; [1, 2, 3] is a column vector. Results render in the same inline form, so they round-trip as input.

Arithmetic

Addition and subtraction are element-wise; * is matrix multiplication; a scalar scales every entry. A / B is A · inverse(B), and A ^ n is repeated multiplication (^0 = identity, ^-1 = inverse).

[1 2, 3 4] + [10 20, 30 40]
[1 2, 3 4] * [5 6, 7 8]
3 * [1 2, 3 4]
[2 4, 6 8] / 2
[1 2, 3 4] ^ 2
[4 7, 2 6] ^ -1
-[1 2, 3 4]

A scalar combined with + or - is broadcast over every entry:

[1 2, 3 4] + 10
10 - [1 2, 3 4]

Functions

transpose([1 2 3, 4 5 6])
determinant([1 2, 3 4])
inverse([4 7, 2 6])
adjugate([1 2, 3 4])
trace([1 2, 3 4])
rank([1 2, 2 4])
rref([1 2 3, 4 5 6, 7 8 9])
minor([1 2 3, 4 5 6, 7 8 10], 1, 1)
cofactor([1 2 3, 4 5 6, 7 8 10], 1, 2)

Build and inspect matrices:

identity(3)
zeros(2, 3)
ones(2, 2)
diag(1, 2, 3)
diag([1 2 3, 4 5 6, 7 8 9])
size([1 2 3, 4 5 6])
rows([1 2 3, 4 5 6])
cols([1 2 3, 4 5 6])
hadamard([1 2, 3 4], [10 20, 30 40])

Solve, measure, and decompose:

linsolve([2 1, 1 3], [5, 10])
norm([3 4])
eigenvalues([2 1, 1 2])
eigenvectors([2 0, 0 3])

Eigenvalues come back as a column vector (sorted by descending real part). When a matrix has complex eigenvalues they are returned as [real imag] rows; eigenvectors supports real spectra only.

Common mistakes