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BerkeleyX: CS-191x Quantum Mechanics and Quantum Computation
Courseware (/courses/BerkeleyX/CS-191x/2013_August/courseware)
Discussion (/courses/BerkeleyX/CS-191x/2013_August/discussion/forum)
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Course Info (/courses/BerkeleyX/CS-191x/2013_August/info)
Wiki (/courses/BerkeleyX/CS-191x/2013_August/course_wiki)
Progress (/courses/BerkeleyX/CS-191x/2013_August/progress)
This diagnostic quiz is designed to help you assess where you are and brush up your understanding of complex numbers and linear
algebra. Your score for this quiz will NOT count into your final grade.
PROBLEM 1 (1/1 point)
?
Help
What is the magnitude of
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You have used 1 of 1 submissions
PROBLEM 2 (1/1 point)
What is the complex conjugate of
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?
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PROBLEM 3 (1/1 point)
Compute
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.
You have used 1 of 1 submissions
▾
PROBLEM 4 (1 point possible)
Select all pairs of matrices that commute. (Matrices
and
are said to commute if
and
and
and
and
and
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PROBLEM 5 (1/1 point)
What is the unit vector in
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which makes an angle of
with both the - and -axes?
You have used 1 of 1 submissions
PROBLEM 6 (1/1 point)
What is a real unit vector in
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that is orthogonal to
You have used 1 of 1 submissions
?
)
PROBLEM 7 (2/2 points)
What is the inner product between the vectors
and
?
And what is the angle between the two vectors, in degrees?
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PROBLEM 8 (1/1 point)
Which of the following are eigenvalues of the matrix
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? Select all that apply.
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PROBLEM 9 (1/1 point)
Which of the following is the eigenvector corresponding to the largest eigenvalue of the above matrix?
Show Answer
You have used 1 of 1 submissions
Interpreting the result
Score range 8~9: You are in good shape!
Score range 6~7: Your understanding of linear algebra is a little rusty, but we expect that you will be in shape for the course if you
spend some time reviewing the questions that you answered incorrectly.
Score range 0~5: You can still take the course if you are well-motivated, but you may need to work hard to fill in the gap in your
understanding of linear algebra as the course progresses.
Review materials
If you are uncomfortable with complex numbers, please read the first three sections of the Wikipedia article
(http://en.wikipedia.org/wiki/Complex_number) on complex numbers.
There is a free online course on linear algebra at Khan Academy (https://www.khanacademy.org/math/linear-algebra). If you did not
perform well on this diagnostic quiz, we recommend that you familiarize yourself with (at least) the following topics in the Khan
Academy course.
Vectors and spaces (https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces)
Vectors
Linear combinations and spans
Subspaces and the basis for a subspace
Vector dot and cross products (but cross product is not required)
Matrix transformations (https://www.khanacademy.org/math/linear-algebra/matrix_transformations)
Functions and linear transformations
Linear transformation examples
Transformations and matrix multiplication
Inverse functions and transformations
Alternate coordinate systems (bases) (https://www.khanacademy.org/math/linear-algebra/alternate_bases)
Change of basis
Orthonormal bases and the Gram-Schmidt Process (you should be comfortable with orthonormal bases, but you don't have to
know Gram-Schmidt)
Eigen-everything
FEEDBACK
During the course, we will send out occasional surveys to better understand the students' experience and improve the course
accordingly. One issue we are trying to understand is the relationship between prior background and the dropout rate in MOOCs.
Your answer to the following optional question will help us in this. Which of the following alternatives most accurately describes how
you plan to proceed after taking the diagnostic quiz?
I am well-prepared for the course.
I need to brush up on some topics, which I plan to do before the course begins.
I need to brush up on some topics, but I plan to catch up after the course begins.
I will decide whether to take the course after seeing the first few week's materials.
I am dropping out of the course.
Any additional comments:
Problem 2: e^{- (pi * i )/3} would be equally good, and Problem 4: first case should be also right.
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