More factorizations

Author: mtfishman

src/fillarrays/kroneckerarray.jl

@@ -11,6 +11,23 @@ const SquareEyeSquareEye{T,A<:SquareEye{T},B<:SquareEye{T}} = KroneckerMatrix{T,
 # Like `adapt` but preserves `Eye`.
 _adapt(to, a::Eye) = a
 
+# Like `similar` but preserves `Eye`.
+function _similar(a::AbstractArray, elt::Type, ax::Tuple)
+  return similar(a, elt, ax)
+end
+function _similar(A::Type{<:AbstractArray}, ax::Tuple)
+  return similar(A, ax)
+end
+function _similar(a::AbstractArray, ax::Tuple)
+  return _similar(a, eltype(a), ax)
+end
+function _similar(a::AbstractArray, elt::Type)
+  return _similar(a, elt, axes(a))
+end
+function _similar(a::AbstractArray)
+  return _similar(a, eltype(a), axes(a))
+end
+
 # Like `similar` but preserves `Eye`.
 function _similar(a::Eye, elt::Type, axs::NTuple{2,AbstractUnitRange})
   return Eye{elt}(axs)

src/fillarrays/linearalgebra.jl

@@ -7,6 +7,9 @@ end
 
 function _mul(a::Eye, b::Eye)
   check_mul_axes(a, b)
+  (size(a, 1) > size(a, 2)) &&
+    (size(b, 1) < size(b, 2)) &&
+    error("This multiplication leads to a projector.")
   T = promote_type(eltype(a), eltype(b))
   return Eye{T}((axes(a, 1), axes(b, 2)))
 end