6868 @test C isa Matrix{T} && size (C) == (minmn, n)
6969 @test N isa Matrix{T} && size (N) == (m, m - minmn)
7070 @test V * C ≈ A
71- @test isisometry (V)
71+ @test isisometric (V)
7272 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
73- @test isisometry (N)
73+ @test isisometric (N)
7474 @test V * V' + N * N' ≈ I
7575
7676 M = LinearMap (A)
8585 @test C isa Matrix{T} && size (C) == (minmn, n)
8686 @test N isa Matrix{T} && size (N) == (m, nullity)
8787 @test V * C ≈ A
88- @test isisometry (V)
88+ @test isisometric (V)
8989 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
90- @test isisometry (N)
90+ @test isisometric (N)
9191 end
9292
9393 for alg_qr in ((; positive = true ), (; positive = false ), LAPACK_HouseholderQR ())
9797 @test C isa Matrix{T} && size (C) == (minmn, n)
9898 @test N isa Matrix{T} && size (N) == (m, m - minmn)
9999 @test V * C ≈ A
100- @test isisometry (V)
100+ @test isisometric (V)
101101 @test LinearAlgebra. norm (A' * N) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
102- @test isisometry (N)
102+ @test isisometric (N)
103103 @test V * V' + N * N' ≈ I
104104 end
105105
110110 @test C2 === C
111111 @test N2 === N
112112 @test V2 * C2 ≈ A
113- @test isisometry (V2)
113+ @test isisometric (V2)
114114 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
115- @test isisometry (N2)
115+ @test isisometric (N2)
116116 @test V2 * V2' + N2 * N2' ≈ I
117117
118118 atol = eps (real (T))
122122 @test C2 != = C
123123 @test N2 != = C
124124 @test V2 * C2 ≈ A
125- @test isisometry (V2)
125+ @test isisometric (V2)
126126 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
127- @test isisometry (N2)
127+ @test isisometric (N2)
128128 @test V2 * V2' + N2 * N2' ≈ I
129129
130130 rtol = eps (real (T))
138138 @test C2 != = C
139139 @test N2 != = C
140140 @test V2 * C2 ≈ A
141- @test isisometry (V2)
141+ @test isisometric (V2)
142142 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
143- @test isisometry (N2)
143+ @test isisometric (N2)
144144 @test V2 * V2' + N2 * N2' ≈ I
145145 end
146146
@@ -150,12 +150,12 @@ end
150150 @test V2 === V
151151 @test C2 === C
152152 @test V2 * C2 ≈ A
153- @test isisometry (V2)
153+ @test isisometric (V2)
154154 if kind != :polar
155155 N2 = @constinferred left_null! (copy! (Ac, A), N; kind = kind)
156156 @test N2 === N
157157 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
158- @test isisometry (N2)
158+ @test isisometric (N2)
159159 @test V2 * V2' + N2 * N2' ≈ I
160160 end
161161
178178 @test C2 != = C
179179 @test N2 != = C
180180 @test V2 * C2 ≈ A
181- @test isisometry (V2)
181+ @test isisometric (V2)
182182 @test LinearAlgebra. norm (A' * N2) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
183- @test isisometry (N2)
183+ @test isisometric (N2)
184184 @test V2 * V2' + N2 * N2' ≈ I
185185 else
186186 @test_throws ArgumentError left_orth! (copy! (Ac, A), (V, C); kind, trunc = (; atol))
204204 @test Vᴴ isa Matrix{T} && size (Vᴴ) == (minmn, n)
205205 @test Nᴴ isa Matrix{T} && size (Nᴴ) == (n - minmn, n)
206206 @test C * Vᴴ ≈ A
207- @test isisometry (Vᴴ; side = :right )
207+ @test isisometric (Vᴴ; side = :right )
208208 @test LinearAlgebra. norm (A * adjoint (Nᴴ)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
209- @test isisometry (Nᴴ; side = :right )
209+ @test isisometric (Nᴴ; side = :right )
210210 @test Vᴴ' * Vᴴ + Nᴴ' * Nᴴ ≈ I
211211
212212 M = LinearMap (A)
220220 @test Vᴴ2 === Vᴴ
221221 @test Nᴴ2 === Nᴴ
222222 @test C2 * Vᴴ2 ≈ A
223- @test isisometry (Vᴴ2; side = :right )
223+ @test isisometric (Vᴴ2; side = :right )
224224 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
225- @test isisometry (Nᴴ; side = :right )
225+ @test isisometric (Nᴴ; side = :right )
226226 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
227227
228228 atol = eps (real (T))
232232 @test Vᴴ2 != = Vᴴ
233233 @test Nᴴ2 != = Nᴴ
234234 @test C2 * Vᴴ2 ≈ A
235- @test isisometry (Vᴴ2; side = :right )
235+ @test isisometric (Vᴴ2; side = :right )
236236 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
237- @test isisometry (Nᴴ; side = :right )
237+ @test isisometric (Nᴴ; side = :right )
238238 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
239239
240240 rtol = eps (real (T))
244244 @test Vᴴ2 != = Vᴴ
245245 @test Nᴴ2 != = Nᴴ
246246 @test C2 * Vᴴ2 ≈ A
247- @test isisometry (Vᴴ2; side = :right )
247+ @test isisometric (Vᴴ2; side = :right )
248248 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
249- @test isisometry (Nᴴ2; side = :right )
249+ @test isisometric (Nᴴ2; side = :right )
250250 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
251251
252252 for kind in (:lq , :polar , :svd )
@@ -255,12 +255,12 @@ end
255255 @test C2 === C
256256 @test Vᴴ2 === Vᴴ
257257 @test C2 * Vᴴ2 ≈ A
258- @test isisometry (Vᴴ2; side = :right )
258+ @test isisometric (Vᴴ2; side = :right )
259259 if kind != :polar
260260 Nᴴ2 = @constinferred right_null! (copy! (Ac, A), Nᴴ; kind)
261261 @test Nᴴ2 === Nᴴ
262262 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
263- @test isisometry (Nᴴ2; side = :right )
263+ @test isisometric (Nᴴ2; side = :right )
264264 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
265265 end
266266
271271 @test Vᴴ2 != = Vᴴ
272272 @test Nᴴ2 != = Nᴴ
273273 @test C2 * Vᴴ2 ≈ A
274- @test isisometry (Vᴴ2; side = :right )
274+ @test isisometric (Vᴴ2; side = :right )
275275 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
276- @test isisometry (Nᴴ2; side = :right )
276+ @test isisometric (Nᴴ2; side = :right )
277277 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
278278
279279 C2, Vᴴ2 = @constinferred right_orth! (copy! (Ac, A), (C, Vᴴ); kind, trunc = (; rtol))
282282 @test Vᴴ2 != = Vᴴ
283283 @test Nᴴ2 != = Nᴴ
284284 @test C2 * Vᴴ2 ≈ A
285- @test isisometry (Vᴴ2; side = :right )
285+ @test isisometric (Vᴴ2; side = :right )
286286 @test LinearAlgebra. norm (A * adjoint (Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit. defaulttol (T)
287- @test isisometry (Nᴴ2; side = :right )
287+ @test isisometric (Nᴴ2; side = :right )
288288 @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
289289 else
290290 @test_throws ArgumentError right_orth! (copy! (Ac, A), (C, Vᴴ); kind, trunc = (; atol))
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