Remove number / vector (#44358)

* Remove number / vector
* Fix test

Author: antoine-levitt

NEWS.md

@@ -46,6 +46,9 @@ Standard library changes
 
 #### LinearAlgebra
 
+* The methods `a / b` and `b \ a` with `a` a scalar and `b` a vector,
+  which were equivalent to `a * pinv(b)`, have been removed due to the
+  risk of confusion with elementwise division ([#44358]).
 * We are now wholly reliant on libblastrampoline (LBT) for calling
   BLAS and LAPACK. OpenBLAS is shipped by default, but building the
   system image with other BLAS/LAPACK libraries is not

stdlib/LinearAlgebra/src/generic.jl

@@ -1142,9 +1142,6 @@ function (/)(A::AbstractVecOrMat, B::AbstractVecOrMat)
     size(A,2) != size(B,2) && throw(DimensionMismatch("Both inputs should have the same number of columns"))
     return copy(adjoint(adjoint(B) \ adjoint(A)))
 end
-# \(A::StridedMatrix,x::Number) = inv(A)*x Should be added at some point when the old elementwise version has been deprecated long enough
-# /(x::Number,A::StridedMatrix) = x*inv(A)
-/(x::Number, v::AbstractVector) = x*pinv(v)
 
 cond(x::Number) = iszero(x) ? Inf : 1.0
 cond(x::Number, p) = cond(x)

stdlib/LinearAlgebra/test/dense.jl

@@ -1108,12 +1108,12 @@ end
 end
 
 function test_rdiv_pinv_consistency(a, b)
-    @test (a*b)/b ≈ a*(b/b) ≈ (a*b)*pinv(b) ≈ a*(b*pinv(b))
-    @test typeof((a*b)/b) == typeof(a*(b/b)) == typeof((a*b)*pinv(b)) == typeof(a*(b*pinv(b)))
+    @test a*(b/b) ≈ (a*b)*pinv(b) ≈ a*(b*pinv(b))
+    @test typeof(a*(b/b)) == typeof((a*b)*pinv(b)) == typeof(a*(b*pinv(b)))
 end
 function test_ldiv_pinv_consistency(a, b)
-    @test a\(a*b) ≈ (a\a)*b ≈ (pinv(a)*a)*b ≈ pinv(a)*(a*b)
-    @test typeof(a\(a*b)) == typeof((a\a)*b) == typeof((pinv(a)*a)*b) == typeof(pinv(a)*(a*b))
+    @test (a\a)*b ≈ (pinv(a)*a)*b ≈ pinv(a)*(a*b)
+    @test typeof((a\a)*b) == typeof((pinv(a)*a)*b) == typeof(pinv(a)*(a*b))
 end
 function test_div_pinv_consistency(a, b)
     test_rdiv_pinv_consistency(a, b)