Fix bug in nullspace when the matrix is empty (#29725)

Make nullspace work for Adjoint

Fixes #28846

(cherry picked from commit 2e2b14c)

stdlib/LinearAlgebra/src/dense.jl

@@ -1332,14 +1332,14 @@ julia> nullspace(M, 2)
  0.0  0.0  1.0
 ```
 """
-function nullspace(A::StridedMatrix, tol::Real = min(size(A)...)*eps(real(float(one(eltype(A))))))
+function nullspace(A::AbstractMatrix, tol::Real = min(size(A)...)*eps(real(float(one(eltype(A))))))
     m, n = size(A)
-    (m == 0 || n == 0) && return Matrix{T}(I, n, n)
+    (m == 0 || n == 0) && return Matrix{eltype(A)}(I, n, n)
     SVD = svd(A, full=true)
-    indstart = sum(SVD.S .> SVD.S[1]*tol) + 1
+    indstart = sum(s -> s .> SVD.S[1]*tol, SVD.S) + 1
     return copy(SVD.Vt[indstart:end,:]')
 end
-nullspace(a::StridedVector, tol::Real = min(size(a)...)*eps(real(float(one(eltype(a)))))) = nullspace(reshape(a, length(a), 1), tol)
+nullspace(a::AbstractVector, tol::Real = min(size(a)...)*eps(real(float(one(eltype(a)))))) = nullspace(reshape(a, length(a), 1), tol)
 
 """
     cond(M, p::Real=2)

stdlib/LinearAlgebra/test/dense.jl

@@ -67,14 +67,17 @@ bimg  = randn(n,2)/2
             end
 
             @testset "Test nullspace" begin
-                a15null = nullspace(copy(a[:,1:n1]'))
+                a15null = nullspace(a[:,1:n1]')
                 @test rank([a[:,1:n1] a15null]) == 10
                 @test norm(a[:,1:n1]'a15null,Inf) ≈ zero(eltya) atol=300ε
                 @test norm(a15null'a[:,1:n1],Inf) ≈ zero(eltya) atol=400ε
                 @test size(nullspace(b), 2) == 0
                 @test size(nullspace(b, 100*εb), 2) == 0
                 @test nullspace(zeros(eltya,n)) == Matrix(I, 1, 1)
                 @test nullspace(zeros(eltya,n), 0.1) == Matrix(I, 1, 1)
+                # test empty cases
+                @test nullspace(zeros(n, 0)) == Matrix(I, 0, 0)
+                @test nullspace(zeros(0, n)) == Matrix(I, n, n)
             end
         end
     end # for eltyb