No classes today.
However, we have office hours (via Zoom) as usual.
Here are three more exercises from the Linear Algebra section of The Highlights Quiz:
**Question 12.** Normalize the vector $\begin{pmatrix} 1 \\ -2 \end{pmatrix}$.
This is example 2.25 on page 55 in Martin's booklet.
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a = np.array([1, -2])
result = a / np.linalg.norm(a)
print(result)
# in WolframAlpha type:
# Normalize[ {1, -2} ]
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(1/np.sqrt(5), -2/np.sqrt(5))
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**Question 13.** Is this a unitary matrix $X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ ?
A matrix is unitary if its transpose conjugate is its inverse.
This is example 2.38 on page 67 in Martin's booklet.
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X = np.array([[0, 1], [1, 0]])
print(np.dot(X, np.conj(X).T))
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**Question 14.** Same question for $Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$
This is part of the same example 2.38 on page 67.
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Y = np.array([[0, -1j], [1j, 0]])
print(np.dot(Y, np.conj(Y).T))
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