Linear Algebra
•Vectors, definition, scalars,
addition, scalar multiplication, inner product (dot product), vector projection, cosine similarity, orthogonal
vectors, normal and orthonormal vectors, vector norm, vector space, linear combination, linear
span, linear independence, basis vectors
•Matrices definition, addition,
transpose, scalar multiplication, matrix multiplication, matrix multiplication properties, hadamard
product, functions, linear transformation, determinant, identity matrix, invertible matrix and inverse, rank,
trace, popular type of matrices- symmetric, diagonal, orthogonal, orthonormal, positive definite
matrix
•Eigen values & eigenvectors,
concept, intuition, significance, how to find Principle component analysis, concept, properties, applications
•Singular value decomposition,
concept, properties, applications
Calculus
•Functions, Scalar derivative,
definition, intuition, common rules of differentiation, chain rule, partial derivatives, Gradient, concept,
intuition, properties, directional derivative
•Vector and matrix calculus, how
to find derivative of scalar-valued, vector-valued function with respect to scalar, vector} four
combinations- Jacobian
•Gradient algorithms,
local/global maxima and minima, saddle point, convex functions, gradient descent algorithms- batch, mini-batch,
stochastic, their performance comparison
Miscellaneous Topics
•Information theory, entropy,
cross entropy, KL divergence, mutual information
•Markov Chain, definition,
transition matrix, stationarity