6
Foreword
Table of Symbols
Symbol
Typical meaning
a, b, c, α, β, γ
x, y, z
A, B, C
x> , A>
A−1
hx, yi
x> y
B = (b1 , b2 , b3 )
B = [b1 , b2 , b3 ]
B = {b1 , b2 , b3 }
Z, N
R, C
Rn
∀x
∃x
a := b
a =: b
a∝b
g◦f
⇐⇒
=⇒
A, C
a∈A
∅
A\B
D
N
Im
0m,n
1m,n
ei
dim
rk(A)
Im(Φ)
ker(Φ)
span[b1 ]
tr(A)
det(A)
|·|
k·k
λ
Eλ
Scalars are lowercase
Vectors are bold lowercase
Matrices are bold uppercase
Transpose of a vector or matrix
Inverse of a matrix
Inner product of x and y
Dot product of x and y
(Ordered) tuple
Matrix of column vectors stacked horizontally
Set of vectors (unordered)
Integers and natural numbers, respectively
Real and complex numbers, respectively
n-dimensional vector space of real numbers
Universal quantifier: for all x
Existential quantifier: there exists x
a is defined as b
b is defined as a
a is proportional to b, i.e., a = constant · b
Function composition: “g after f ”
If and only if
Implies
Sets
a is an element of set A
Empty set
A without B : the set of elements in A but not in B
Number of dimensions; indexed by d = 1, . . . , D
Number of data points; indexed by n = 1, . . . , N
Identity matrix of size m × m
Matrix of zeros of size m × n
Matrix of ones of size m × n
Standard/canonical vector (where i is the component that is 1)
Dimensionality of vector space
Rank of matrix A
Image of linear mapping Φ
Kernel (null space) of a linear mapping Φ
Span (generating set) of b1
Trace of A
Determinant of A
Absolute value or determinant (depending on context)
Norm; Euclidean, unless specified
Eigenvalue or Lagrange multiplier
Eigenspace corresponding to eigenvalue λ
Draft (2022-01-11) of “Mathematics for Machine Learning”. Feedback: https://mml-book.com.
7
Foreword
Symbol
Typical meaning
x⊥y
V
V⊥
PN
x
QNn=1 n
n=1 xn
θ
Vectors x and y are orthogonal
Vector space
Orthogonal complement of vector space V
Sum of the xn : x1 + . . . + xN
Product of the xn : x1 · . . . · xN
Parameter vector
Partial derivative of f with respect to x
Total derivative of f with respect to x
Gradient
The smallest function value of f
The value x∗ that minimizes f (note: arg min returns a set of values)
Lagrangian
Negative log-likelihood
Binomial coefficient, n choose k
Variance of x with respect to the random variable X
Expectation of x with respect to the random variable X
Covariance between x and y .
X is conditionally independent of Y given Z
Random variable X is distributed according to p
Gaussian distribution with mean µ and covariance Σ
Bernoulli distribution with parameter µ
Binomial distribution with parameters N, µ
Beta distribution with parameters α, β
∂f
∂x
df
dx
∇
f∗ = minx f (x)
x∗ ∈ arg minx f (x)
L
L
n
k
VX [x]
EX [x]
CovX,Y [x, y]
X⊥
⊥ Y |Z
X∼p N µ, Σ
Ber(µ)
Bin(N, µ)
Beta(α, β)
Table of Abbreviations and Acronyms
Acronym
Meaning
e.g.
GMM
i.e.
i.i.d.
MAP
MLE
ONB
PCA
PPCA
REF
SPD
SVM
Exempli gratia (Latin: for example)
Gaussian mixture model
Id est (Latin: this means)
Independent, identically distributed
Maximum a posteriori
Maximum likelihood estimation/estimator
Orthonormal basis
Principal component analysis
Probabilistic principal component analysis
Row-echelon form
Symmetric, positive definite
Support vector machine
©2021 M. P. Deisenroth, A. A. Faisal, C. S. Ong. Published by Cambridge University Press (2020).