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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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Task/Conjugate-transpose/J/conjugate-transpose-1.j Normal file
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ct =: +@|: NB. Conjugate transpose (ct A is A_ct)

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Task/Conjugate-transpose/J/conjugate-transpose-2.j Normal file
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X =: +/ . * NB. Matrix Multiply (x)
HERMITIAN =: 3 2j1 ,: 2j_1 1
(-: ct) HERMITIAN NB. A_ct = A
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NORMAL =: 1 1 0 , 0 1 1 ,: 1 0 1
((X~ -: X) ct) NORMAL NB. A_ct x A = A x A_ct
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UNITARY =: (-:%:2) * 1 1 0 , 0j_1 0j1 0 ,: 0 0 0j1 * %:2
(ct -: %.) UNITARY NB. A_ct = A^-1
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Task/Conjugate-transpose/J/conjugate-transpose-3.j Normal file
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HERMITIAN;NORMAL;UNITARY
+--------+-----+--------------------------+
| 3 2j1|1 1 0| 0.707107 0.707107 0|
|2j_1 1|0 1 1|0j_0.707107 0j0.707107 0|
| |1 0 1| 0 0 0j1|
+--------+-----+--------------------------+
NB. In J, PjQ is P + Q*i and the 0.7071... is sqrt(2)
hermitian=: -: ct
normal =: (X~ -: X) ct
unitary=: ct -: %.
(hermitian,normal,unitary)&.>HERMITIAN;NORMAL;UNITARY
+-----+-----+-----+
|1 1 0|0 1 0|0 1 1|
+-----+-----+-----+