Function gram_matrix 

pub const fn gram_matrix<const M: usize, const N: usize>(
    vectors: &[Vector<N>; M],
) -> Result<Matrix<M>, LaError>

Construct a stack-backed Matrix<M> of pairwise vector dot products.

A Gram matrix records pairwise inner products: diagonal entries are squared vector lengths, and off-diagonal entries encode their relative angles. The input contains M finite-by-construction Vector<N> values. If V has these vectors as rows, the mathematical Gram matrix is G = V Vᵀ, with G[i,j] = vectors[i] · vectors[j]. In exact real arithmetic and for M ≤ N, its determinant is the squared volume of the spanned parallelotope. For edges from one simplex vertex, the simplex volume is sqrt(det(G)) / M!; this also handles facets embedded in higher dimensions. See REFERENCES.md [16] for the Gram determinant and volume interpretation.

Each upper-triangle dot product is computed once using Vector::dot’s left-to-right fused multiply-add reduction and copied to the other triangle, giving bit-for-bit symmetry. No absolute rounding-error bound is provided. Rounding and underflow can destroy positive semidefiniteness or rank; this operation proves neither positive definiteness nor affine independence. Matrix::ldlt retains its symmetry and positive-definiteness preconditions. Forming a Gram matrix squares the spectral condition number of an exact input with full row rank. See the floating-point discussion in REFERENCES.md [9-11].

M and N are independent, with no dimension cap (including dimensions through 8); storage is O(M²) and work is O(M²(N + 1)), including output initialization when N = 0. M = 0 returns an empty matrix; N = 0 returns an all-zero matrix. No optional feature is required.

Errors

Returns LaError::NonFinite if a dot-product accumulator overflows, even when the exact result would be finite after cancellation. The error preserves Vector::dot’s Computation origin, VectorDotProduct operation, and first failing reduction Step. The step indexes the vector coordinate, not the output matrix cell. Pairs are visited in upper-triangle row order.

Examples

use la_stack::prelude::*;
let vectors = [Vector::try_new([1.0, 0.0, 0.0])?,
               Vector::try_new([0.0, 2.0, 0.0])?];
let gram = gram_matrix(&vectors)?;
assert_eq!(gram.as_rows(), &[[1.0, 0.0], [0.0, 4.0]]);
assert_eq!(gram.ldlt(Tolerance::try_new(0.0)?)?.det()?, 4.0);