@@ -31,7 +31,7 @@ function test_left_orthnull(
3131 @test isisometric (V)
3232 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
3333 @test isisometric (N)
34- @test V * V ' + N * N ' ≈ I
34+ @test collect (V) * collect (V) ' + collect (N) * collect (N) ' ≈ I
3535
3636 M = LinearMap (A)
3737 # broken
@@ -64,7 +64,7 @@ function test_left_orthnull(
6464 @test isisometric (V)
6565 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
6666 @test isisometric (N)
67- @test V * V ' + N * N ' ≈ I
67+ @test collect (V) * collect (V) ' + collect (N) * collect (N) ' ≈ I
6868
6969 # passing an algorithm
7070 if ! isa (A, Diagonal)
@@ -77,7 +77,7 @@ function test_left_orthnull(
7777 @test isisometric (V)
7878 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
7979 @test isisometric (N)
80- @test V * V ' + N * N ' ≈ I
80+ @test collect (V) * collect (V) ' + collect (N) * collect (N) ' ≈ I
8181 end
8282
8383 Ac = similar (A)
@@ -87,7 +87,7 @@ function test_left_orthnull(
8787 @test isisometric (V2)
8888 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
8989 @test isisometric (N2)
90- @test V2 * V2 ' + N2 * N2 ' ≈ I
90+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
9191
9292 # doesn't work on AMD...
9393 atol = eps (real (eltype (T)))
@@ -97,7 +97,7 @@ function test_left_orthnull(
9797 @test isisometric (V2)
9898 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
9999 @test isisometric (N2)
100- @test V2 * V2 ' + N2 * N2 ' ≈ I
100+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
101101
102102 if (T <: Number || T <: Diagonal{<:Number, <:Vector} )
103103 rtol = eps (real (eltype (T)))
@@ -111,7 +111,7 @@ function test_left_orthnull(
111111 @test isisometric (V2)
112112 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
113113 @test isisometric (N2)
114- @test V2 * V2 ' + N2 * N2 ' ≈ I
114+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
115115 end
116116 end
117117
@@ -126,7 +126,7 @@ function test_left_orthnull(
126126 N2 = @testinferred left_null! (copy! (Ac, A), N; alg)
127127 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
128128 @test isisometric (N2)
129- @test V2 * V2 ' + N2 * N2 ' ≈ I
129+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
130130 end
131131
132132 # with kind and tol kwargs
@@ -140,7 +140,7 @@ function test_left_orthnull(
140140 @test isisometric (V2)
141141 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
142142 @test isisometric (N2)
143- @test V2 * V2 ' + N2 * N2 ' ≈ I
143+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
144144
145145 # broken
146146 # V2, C2 = @testinferred left_orth!(copy!(Ac, A), (V, C); alg = alg, trunc = (; rtol))
@@ -150,7 +150,7 @@ function test_left_orthnull(
150150 @test isisometric (V2)
151151 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
152152 @test isisometric (N2)
153- @test V2 * V2 ' + N2 * N2 ' ≈ I
153+ @test collect (V2) * collect (V2) ' + collect (N2) * collect (N2) ' ≈ I
154154 end
155155 else
156156 @test_throws ArgumentError left_orth! (copy! (Ac, A), (V, C); alg, trunc = (; atol))
@@ -183,7 +183,7 @@ function test_right_orthnull(
183183 @test isisometric (Vᴴ; side = :right )
184184 @test LinearAlgebra. norm (A * adjoint (Nᴴ)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
185185 @test isisometric (Nᴴ; side = :right )
186- @test Vᴴ ' * Vᴴ + Nᴴ ' * Nᴴ ≈ I
186+ @test collect (Vᴴ) ' * collect (Vᴴ) + collect (Nᴴ) ' * collect (Nᴴ) ≈ I
187187
188188 M = LinearMap (A)
189189 # broken
@@ -198,7 +198,7 @@ function test_right_orthnull(
198198 @test isisometric (Vᴴ2; side = :right )
199199 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
200200 @test isisometric (Nᴴ; side = :right )
201- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
201+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
202202
203203 if (T <: Number || T <: Diagonal{<:Number, <:Vector} )
204204 atol = eps (real (eltype (T)))
@@ -208,7 +208,7 @@ function test_right_orthnull(
208208 @test isisometric (Vᴴ2; side = :right )
209209 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
210210 @test isisometric (Nᴴ; side = :right )
211- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
211+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
212212
213213 rtol = eps (real (eltype (T)))
214214 C2, Vᴴ2 = @testinferred right_orth! (copy! (Ac, A), (C, Vᴴ); trunc = (; rtol))
@@ -217,7 +217,7 @@ function test_right_orthnull(
217217 @test isisometric (Vᴴ2; side = :right )
218218 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
219219 @test isisometric (Nᴴ2; side = :right )
220- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
220+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
221221 end
222222
223223 for alg in (:lq , :polar , :svd )
@@ -231,7 +231,7 @@ function test_right_orthnull(
231231 Nᴴ2 = @testinferred right_null! (copy! (Ac, A), Nᴴ; alg = alg)
232232 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
233233 @test isisometric (Nᴴ2; side = :right )
234- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
234+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
235235 end
236236
237237 if alg == :svd
@@ -244,7 +244,7 @@ function test_right_orthnull(
244244 @test isisometric (Vᴴ2; side = :right )
245245 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
246246 @test isisometric (Nᴴ2; side = :right )
247- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
247+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
248248
249249 # broken
250250 # C2, Vᴴ2 = @testinferred right_orth!(copy!(Ac, A), (C, Vᴴ); alg = alg, trunc = (; rtol))
@@ -254,7 +254,7 @@ function test_right_orthnull(
254254 @test isisometric (Vᴴ2; side = :right )
255255 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
256256 @test isisometric (Nᴴ2; side = :right )
257- @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
257+ @test collect ( Vᴴ2) ' * collect ( Vᴴ2) + collect ( Nᴴ2) ' * collect ( Nᴴ2) ≈ I
258258 end
259259 else
260260 @test_throws ArgumentError right_orth! (copy! (Ac, A), (C, Vᴴ); alg, trunc = (; atol))
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