How can you determine the eigenvalues for a given matrix? Can you provide an example?

How can you tell if a system of two linear equations has a unique solution, many solutions, or no solutions?

What distinguishes the Cross Product from the Dot Product?

What is ( Ax = b ) and when does it have a unique solution?

Explain the concept of a norm.

What are the different ways to measure the magnitude of a vector?

Can the count of non-zero elements in a vector be considered a norm? If not, why?

How would you diagonalize a matrix?

How do matrices differ from tensors?

Is the eigendecomposition of a real matrix always unique? If not, how can it be represented?

Explain the Hadamard product of two matrices.

What is the determinant of a square matrix and how do you calculate it?

Define a positive definite matrix.

What is an Orthogonal Matrix? Why is it computationally preferred?

What are positive definite, negative definite, positive semi-definite, and negative semi-definite matrices?

Under what conditions does a matrix have an inverse?

What does broadcasting mean in the context of Linear Algebra?

Explain the concept of span and linear dependence

How can you compute the Singular Value Decomposition (SVD) of a matrix M?

What is the purpose of the Moore-Penrose Pseudoinverse and how can one compute it?

What are Singular Values, and what are Left and Right Singular Vectors?

When should you use L1-norm over L2-norm for regularization?

Why is Singular Value Decomposition (SVD) preferred over Eigendecomposition?