LINEAR ALGEBRA AND OPTIMIZATION
FOR MACHINE LEARNING FINAL PAPER
TESTED QUESTIONS WITH VERIFIED
ANSWERS COMPLETE STUDY SHEET
●● (Differential) Calculus
Answer: Minimising cost functions (a scalar function of several
variables that typically measures how poorly our model fits the data) to
study their continuous change
●● Probability
Answer: characterising uncertainty in our learning environments
stochastically
●● Statistics
Answer: Drawing conclusions based on the analysis of data
●● Vector space (not essential to know formal definition)
Answer: the setting in which linear algebra takes place; A set of vectors
with defined addition and scalar multiplication e.g. polynomials,
complex. They must satisfy various closure properties, commutativity,
associativity, distributivity etc.
, ●● Scalar
Answer: real number denoted by lowercase letter
●● Linear independence
Answer: no nontrivial linear combination. of the vectors that equalsthe
zero vector exists
●● Span of V
Answer: the set of all vectors that can be expressed as a combination of
the vectors in V
●● Basis for V
Answer: a set of linearly independent vectors which span the whole of V
●● Dimension
Answer: the number of vectors in a basis
●● Euclidean space
Answer: the vector space formed by the n-tuple vectors of real numbers
●● Standard basis
Answer: a special orthonormal basis in which each basis vector has a
nonzero entry with value 1
FOR MACHINE LEARNING FINAL PAPER
TESTED QUESTIONS WITH VERIFIED
ANSWERS COMPLETE STUDY SHEET
●● (Differential) Calculus
Answer: Minimising cost functions (a scalar function of several
variables that typically measures how poorly our model fits the data) to
study their continuous change
●● Probability
Answer: characterising uncertainty in our learning environments
stochastically
●● Statistics
Answer: Drawing conclusions based on the analysis of data
●● Vector space (not essential to know formal definition)
Answer: the setting in which linear algebra takes place; A set of vectors
with defined addition and scalar multiplication e.g. polynomials,
complex. They must satisfy various closure properties, commutativity,
associativity, distributivity etc.
, ●● Scalar
Answer: real number denoted by lowercase letter
●● Linear independence
Answer: no nontrivial linear combination. of the vectors that equalsthe
zero vector exists
●● Span of V
Answer: the set of all vectors that can be expressed as a combination of
the vectors in V
●● Basis for V
Answer: a set of linearly independent vectors which span the whole of V
●● Dimension
Answer: the number of vectors in a basis
●● Euclidean space
Answer: the vector space formed by the n-tuple vectors of real numbers
●● Standard basis
Answer: a special orthonormal basis in which each basis vector has a
nonzero entry with value 1
