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Mathematics & Statistics

Vector and Matrices

Interview questions on Vector and Matrices.

41 questions

All subtopicsVectorMatrices

Matrices

Q2. Define the condition under which we can multiply two matrices?

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Matrices

Q5. How is the Hadamard product different from the dot product?

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Matrices

Q15. Why do we say that matrices are linear transformations?

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Matrices

Q16. Do all matrices have an inverse? Is the inverse of a matrix always unique?

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Matrices

Q19. When we should use $L^1$ norm instead of $L^2$ norm?

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Matrices

Q22. Can you write the dot product of two vectors in terms of their norms?

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Matrices

Q23. Define following type of matrices:

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  • Diagonal Matrix
  • Symmetric Matrix
  • Orthogonal Matrix

Matrices

Q26. Express the eigen decomposition of square matrix $\mathbf{A}$ ?

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Matrices

Q29. What is the benefit of using Singular Value Decomposition(SVD) over eigenvalue decomposition?

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Matrices

Q31. What is the relationship between eigen-value decomposition and SVD?

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Matrices

Q35. What does the absolute value of the determinant depicts?

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Matrices

Q36. What happens to the determinant of a matrix if we multiply one of its rows by a scalar $t×R$ ?

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Matrices

Q37. A $4×4$ matrix has four eigenvalues $3, 3, 2, −1$. What can we say about the trace and the determinant of this matrix?

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Matrices

Q38. Given the following matrix:

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[14−2−13235−6]\begin{bmatrix} 1 & 4 & -2 \\\\ -1 & 3 & 2 \\\\ 3 & 5 & -6 \end{bmatrix} Without explicitly using the equation for calculating determinants, what can we say about this matrix’s determinant?

Matrices

Q39. What’s the difference between the covariance matrix $A^TA$ and the Gram matrix $AA^T$?

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Matrices

Q40. Given $A∈R^{n×m}$ and $b∈R^n$1. Find$ x $such that:$ Ax=b$.

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  1. When does this have a unique solution?
  2. Why is it when AA has more columns than rows, Ax=bAx=b has multiple solutions?
  3. Given a matrix AA with no inverse. How would you solve the equation Ax=bAx=b? What is the pseudo inverse and how to calculate it?

Matrices

Q41. Given a very large symmetric matrix $A$ that doesn’t fit in memory, say $A∈R^{1M×1M}$ and a function $f$ that can quickly compute $f(x)=Ax$ for $x∈R1M$. Find the unit vector$ x $so that$ x^TAx$ is minimal.

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