chore: add comment providing details on the householder fix.
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@ -34,7 +34,17 @@ pub fn reflection_axis_mut<T: ComplexField, D: Dim, S: StorageMut<T, D>>(
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if !factor.is_zero() {
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column.unscale_mut(factor.sqrt());
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// Normalize again, making sure the vector is unit-sized.
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// If `factor` had a very small value, the first normalization
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// (dividing by `factor.sqrt()`) might end up with a slightly
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// non-unit vector (especially when using 32-bits float).
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// Decompositions strongly rely on that unit-vector property,
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// so we run a second normalization (that is much more numerically
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// stable since the norm is close to 1) to ensure it has a unit
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// size.
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let _ = column.normalize_mut();
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(-signed_norm, true)
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} else {
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// TODO: not sure why we don't have a - sign here.
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