Linear algebra (core-lite)

Core matten provides small linalg-adjacent helpers, not a linear algebra backend. matten prioritizes PoC ergonomics, not numerical linear algebra performance or stability leadership.

matten offers exactly three linalg-adjacent helpers (RFC-041), alongside the dot/matmul already in Reductions and matrix multiplication:

• norm — L2 / Frobenius norm over all elements.
• trace — diagonal sum of a rank-2 tensor.
• outer — rank-1 × rank-1 outer product.

norm

#![allow(unused)]
fn main() {
Tensor::norm(&self) -> f64
}

The L2 / Frobenius norm over all elements: sqrt(sum(x_i^2)). It works at any rank — for a matrix this is the Frobenius norm. NaN propagates (any NaN element yields NaN). No overflow-avoidance scaling is applied, so extreme magnitudes may overflow to infinity.

Like the other value reductions (sum, mean), norm has no try_* form; it panics on a dynamic tensor (convert with try_numeric() first).

norm([3, 4])          = 5            // sqrt(9 + 16)
norm([[1, 2], [2, 4]]) = 5           // Frobenius: sqrt(1 + 4 + 4 + 16)

trace

#![allow(unused)]
fn main() {
Tensor::trace(&self) -> f64
Tensor::try_trace(&self) -> Result<f64, MattenError>
}

The sum of the diagonal of a rank-2 tensor. Rectangular matrices are allowed: the trace sums self[i, i] for i in 0..min(rows, cols).

trace([[1, 2], [3, 4]])             = 5   // 1 + 4
trace([[1, 2, 3], [4, 5, 6]])       = 6   // min(2,3)=2 -> self[0,0] + self[1,1]

try_trace returns MattenError::Shape if the tensor is not rank-2, or MattenError::Unsupported on a dynamic tensor; trace panics in those cases.

outer

#![allow(unused)]
fn main() {
Tensor::outer(&self, other: &Tensor) -> Tensor
Tensor::try_outer(&self, other: &Tensor) -> Result<Tensor, MattenError>
}

The outer product of two rank-1 tensors: out[i, j] = self[i] * other[j], with shape [self.len(), other.len()]. The output is checked against MattenLimits before allocation.

[1, 2, 3] ⊗ [4, 5]  ->  [[4, 5], [8, 10], [12, 15]]   // shape [3, 2]

try_outer returns MattenError::Shape if either input is not rank-1, MattenError::Unsupported on a dynamic tensor, or MattenError::Allocation if the result exceeds the limit; outer panics in those cases.

Out of scope for core

The following are intentionally not in core matten (RFC-041 §5):

inverse        determinant     solve          least_squares
eigenvalues    eigenvectors    SVD            QR
LU             Cholesky        sparse         BLAS / LAPACK

For serious numerical linear algebra, use a specialized crate such as nalgebra or ndarray-linalg. A future matten-nalgebra / matten-ndarray-linalg bridge would require its own RFC.

Example

See 15_norm_trace_outer.rs for a runnable walkthrough.