Consider the 2 x 2 matrix defined by aoi a U . (5) ао — iд .a where ao is a real number, and a is a three-dimensional vector with real components. a. Prove that U is unitary and unimodular b. In general, a 2 x 2 unitary unimodular matrix represents a rotation in three dimensions. Find the axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3
Consider the 2 x 2 matrix defined by aoi a U . (5) ао — iд .a where ao is a real number, and a is a three-dimensional vector with real components. a. Prove that U is unitary and unimodular b. In general, a 2 x 2 unitary unimodular matrix represents a rotation in three dimensions. Find the axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3
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![Consider the 2 x 2 matrix defined by
aoi a
U
.
(5)
ао — iд .a
where ao is a real number, and a is a three-dimensional vector with real components.
a. Prove that U is unitary and unimodular
b. In general, a 2 x 2 unitary unimodular matrix represents a rotation in three dimensions. Find the
axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9faf22f-10a8-4cb5-bec9-d63452f6293a%2Fe13ac713-9a22-4ca0-b1c1-b52ac807263a%2Fn2xyu6e.png&w=3840&q=75)
Transcribed Image Text:Consider the 2 x 2 matrix defined by
aoi a
U
.
(5)
ао — iд .a
where ao is a real number, and a is a three-dimensional vector with real components.
a. Prove that U is unitary and unimodular
b. In general, a 2 x 2 unitary unimodular matrix represents a rotation in three dimensions. Find the
axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3
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