mat = matrix([[0,1],[1,0]]) #creates a pauli matrix
u = exp(i*mat)# creates an unitary matrix
print ((u.H)*u).n() # u*u evaluated numerically
$U^\dagger U$ does not return the identity. why?
sage output-
[4.44305526025399e6 4.44305526025388e6]
[4.44305526025388e6 4.44305526025399e6]
Mhh strange: For me this code works fine on sagenb.org: http://sagenb.org/home/pub/4689
On the sage Version which is installed on my PC (sage 4.7.1) the code throws an attribute Error: Attribute H unknown. However replacing .H by .conjugate_transpose() solves the problem there:
sage: mat = matrix([[0,1],[1,0]]) #creates a pauli matrix
sage: u = exp(i*mat) # creates an unitary matrix
sage: show(((u.conjugate_transpose())*u).n()) # u*u evaluated numerically
returns a unity matrix. Maybe the version you work with doesn't properly support .H either?
The U.H abbreviation for U.conjugate_transpose() was added only relatively recently.
Asked: 2012-04-12 05:11:11 +0100
Seen: 5,889 times
Last updated: Apr 12 '12
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the weirdest thing - it works now! hmm .. i was using the sagenb.org worksheet interface. thanks!