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Mathematics & Statistics

Vector and Matrices

Interview questions on Vector and Matrices.

10 questions

All subtopicsVectorMatrices

Vector

Q1. Define following terms

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  1. Scalers
  2. Vectors
  3. Matrices
  4. Tensors

Vector

Q2. What is broadcasting in matrices in context of deep learning?

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Vector

Q3. Dot product 1. What’s the geometric interpretation of the dot product of two vectors? 1. Given a vector $u $, find vector$ v $of unit length such that the dot product of$ u $and$ v$ is maximum.

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Vector

Q4. Outer product

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  1. Given two vectors a=[3,2,1]a=[3,2,1] and b=[−1,0,1]b=[−1,0,1]. Calculate the outer productaTb a^Tb ?
  2. Give an example of how the outer product can be useful in ML.

Vector

Q5. What does it mean for two vectors to be linearly independent?

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Vector

Q6. Given two sets of vectors $A=a_1,a_2,a_3,...,a_n$ and $B=b_1,b_2,b_3,...,b_m$. How do you check that they share the same basis?

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Vector

Q9. Given $n$ vectors, each of $d$ dimensions. What is the dimension of their span?

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Vector

Q10. Norms and metrics

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  1. What's the norm? What is L0,L1,L2,LnormL_0,L_1,L_2,L_{norm}?
  2. How do norms and metrics differ? Given a norm, make a metric. Given a metric, can we make a norm?