What are the entries of the identity matrix Iₙ?

What is a square matrix with linearly dependent columns called?

What is the span of a set of vectors?

What is the inverse of diag(2, 5)?

A real matrix A has 3 rows and 5 columns. Which set does it belong to?

A linear system Ax = b has two different solutions. How many solutions does it have in total?

In C = AB, what is the entry Cᵢ,ⱼ?

When does a square diagonal matrix have an inverse?

Which matrices have a singular value decomposition?

What is the max norm ‖x‖∞ of x = [2, −9, 5]ᵀ?

A is 3 × 4 and B is 4 × 2. What is the shape of AB?

The Frobenius norm of a matrix is the analogue of which vector norm?

A is 4 × 1 and B is 1 × 4. What is the shape of BA?

x and y are nonzero vectors with xᵀy = 0. What is the angle between them?

det(A) = 0. What does multiplying by A do to space?

When does the book say the L¹ norm is preferred to the squared L² norm?

What is the Frobenius norm of the 2 × 2 matrix with rows [2, 0] and [1, 2]?

The right-singular vectors of A are the eigenvectors of which matrix?

Which conditions together guarantee that a matrix A has an inverse?

What is the dot product of x = [2, −1, 3]ᵀ and y = [4, 0, 1]ᵀ?

A 3 × 3 matrix has eigenvalues 2, 3 and 4. What is its determinant?

A has more rows than columns, and Ax = y has no exact solution. What does x = A⁺y give?

Q is an orthogonal matrix. What is Q⁻¹?

A is invertible. What is the solution of Ax = b?

Which expression equals (AB)ᵀ?

Why does the book advise against computing A⁻¹ to solve Ax = b in most software?

In PCA with decoding matrix D, what is the optimal code c for an input x?

The eigenvalues of AᵀA are 9, 4 and 0. What are the nonzero singular values of A?

How do practical algorithms compute the pseudoinverse A⁺?

Which property does matrix multiplication NOT have in general?

Which equality holds for any matrices A, B, C whose products are defined?

What kind of object is the dot product of two vectors?

What must be true of the rows of an orthogonal matrix?

If A is a 4 × 2 matrix, what is the shape of Aᵀ?

Why is the number of nonzero entries of a vector (the “L⁰ norm”) not really a norm?

What does a positive semidefinite matrix A guarantee for every vector x?

What is the product of two same-shape matrices that multiplies matching entries called?

For the matrix product AB to be defined, what must be true?

What constraint does PCA put on the columns of the decoding matrix D?

What is the L¹ norm of x = [−2, 5, 1]ᵀ?

A is the 2 × 2 matrix with rows [2, 1] and [1, 2], and v = [1, 1]ᵀ. Av = λv for which eigenvalue λ?

What is the trace of the 2 × 2 matrix with rows [2, 1] and [0, 5]?

A matrix has eigenvalues 3, 1 and 0. Which kind of matrix is it?

When is a nonzero vector v an eigenvector of a square matrix A?

A real symmetric matrix is written A = QΛQᵀ. What kind of matrix is Q?

In the linear system Ax = b with A ∈ ℝ⁵ˣ³, how many unknowns are there?

In deep learning’s shorthand C = A + b, where A is a matrix and b a vector, what happens to b?

A ∈ ℝᵐˣⁿ. What is a necessary condition for Ax = b to have a solution for every b ∈ ℝᵐ?

v is an eigenvector of A with eigenvalue λ. What is the eigenvalue of the eigenvector 5v?

Ax = b has a solution exactly when b lies in which set?

What is the implicit copying of b to many locations in C = A + b called?

A has more columns than rows, so Ax = y has many solutions. Which one does x = A⁺y return?

What is the L² (Euclidean) norm of x = [6, −8]ᵀ?

A square matrix is singular if and only if…

A is 5 × 3 and A = UDVᵀ is its SVD. What is the shape of D?

A is real and symmetric. What is the maximum of xᵀAx over all unit vectors x?

Which vector is the first principal component of a data matrix X (one example per row)?

A matrix A is symmetric when…

In the Deep Learning book, what is a tensor?

In ℝ³, at most how many nonzero vectors can be mutually orthogonal?