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Top 42 Linear Algebra Interview Questions
Entry Junior Mid Senior Expert
Linear Algebra Theoretical Questions
Q1:
How do you find eigenvalues of a matrix? Could you provide an example?
Junior
Q2:
What is ? When does has a unique solution?
Junior
Q3:
What's the difference between Cross Product and Dot Product?
Junior
Q4:
What is Frobenius norm?
Junior
Q5:
At what conditions does the inverse of a diagonal matrix exist?
Junior
Q6:
What's the normal vector to the surface S provide below?
Junior
Q7:
How do you know if a system of two linear equations has one solution, multiple solutions or no solutions?
Junior
Q8:
What are positive definite, negative definite, positive semi definite and negative semi definite matrices?
Mid Q9:
What is an Orthogonal Matrix? Why is computationally preferred?
Mid Q10:
At what conditions does the inverse of a matrix exist?
Mid Q11:
What is the determinant of a square matrix? How is it calculated?
Mid Q12:
Related To: PCA, Dimensionality Reduction
Why is Centering and Scaling the data important before performing PCA?
Related To: PCA, Dimensionality Reduction Mid Mid Q14:
Discuss span and linear dependence
Mid Q15:
What are the conditions that a norm function has to satisfy?
Mid Q16:
How many ways of measure a vector do you know?
Mid Q17:
Can the number of nonzero elements in a vector be defined as norm? If no, why?
Mid Q18:
How do you diagonalize a matrix?
Mid Q19:
Diagonalize, if it's possible, the following matrix
Mid Q20:
What is Hadamard product of two matrices?
Mid Q21:
What’s the difference between a Matrix and a Tensor?
Mid Q22:
Is the Eigendecomposition guaranteed to be unique for a real matrix? If not, then how do we represent it?
Mid Q23:
What happens if we transform a vector z using a positive definite matrix?
Mid Mid Q25:
Why do we use Singular Value Decomposition? Why not just use Eigendecomposition?
Senior Q26:
When performing regularization, when would you choose L1-norm over L2-norm?
Senior Q27:
What are Singular Eigenvalues, Left Singulars and Right Singulars?
Senior Q28:
Why would you use the Moore-Penrose Pseudoinverse and how would you calculate it?
Senior Q29:
Given a matrix M, how do you calculate its Singular Value Decomposition?
Senior Linear Algebra Practical Challenges
Q1:
Prove that the following matrices are inverses
Junior Q2:
For which value of q the following set of linear equations can have a non-trivial solution?
q the following set of linear equations can have a non-trivial solution? Junior Q3:
When are two vectors x and y orthogonal?
x and y orthogonal? Junior Q4:
Find the values of k that make the following matrices positive definite
k that make the following matrices positive definite Junior Q5:
Find the value of k such that the vectors u and v are orthogonal
k such that the vectors u and v are orthogonal Mid Q6:
Compute the adjugate of the following matrix
Mid Q7:
Solve the following system using determinants or the Cramer's rule
Mid Q8:
Find the inverse of the following matrix
Mid Q9:
Compute the cofactors of the following matrix
Mid Q10:
Diagonalize the following matrix
Mid Q11:
Determine which of the following matrices is normal
Mid Q12:
How do you find the inverse of a 2x2 matrix?
2x2 matrix? Mid Q13:
How would you find the inverse of an nxn matrix?
nxn matrix? Senior 
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