Linear algebra

Matrices

ti.Matrix is for small matrices (e.g. 3x3) only. If you have 64x64 matrices, you should consider using a 2D tensor of scalars.
ti.Vector is the same as ti.Matrix, except that it has only one column.
Differentiate element-wise product * and matrix product @.
ti.transposed(A)
ti.inverse(A)
ti.Matrix.abs(A)
ti.trace(A)
ti.determinant(A, type)
A.cast(type)
R, S = ti.polar_decompose(A, ti.f32)
U, sigma, V = ti.svd(A, ti.f32) (Note that sigma is a 3x3 diagonal matrix)

Vectors are special matrices with only 1 column. In fact, ti.Vector is just an alias of ti.Matrix.

Dot product: a.dot(b), where a and b are vectors. ti.transposed(a) @ b will give you a matrix of size 1x1, which is not a scalar.
Outer product: ti.outer_product(a, b)
l-2 norm: a.norm(eps = 0)
- returns sqrt(\sum_i(x_i ^ 2) + eps)
- Set eps = 1e-5 for example, to safe guards the operator's gradient on zero vectors during differentiable programming.