List of Main Symbols ==================== The main symbols used in this book are listed below. Numbers ------- +--------------------+--------+ | Symbol | Type | +====================+========+ | :math:x | Scalar | +--------------------+--------+ | :math:\mathbf{x} | Vector | +--------------------+--------+ | :math:\mathbf{X} | Matrix | +--------------------+--------+ | :math:\mathsf{X} | Tensor | +--------------------+--------+ Sets ---- +-----------------------------------+-----------------------------------+ | Symbol | Type | +===================================+===================================+ | :math:\mathcal{X} | Set | +-----------------------------------+-----------------------------------+ | :math:\mathbb{R} | Real numbers | +-----------------------------------+-----------------------------------+ | :math:\mathbb{R}^n | Vectors of real numbers in | | | :math:n dimensions | +-----------------------------------+-----------------------------------+ | :math:\mathbb{R}^{a \times b} | Matrix of real numbers with | | | :math:a rows and :math:b | | | columns | +-----------------------------------+-----------------------------------+ Operators --------- +-------------------------+--------------------------------------------+ | Symbol | Type | +=========================+============================================+ | :math:\mathbf{(\cdot)} | Vector or matrix transposition | | ^\top | | +-------------------------+--------------------------------------------+ | :math:\odot | Element-wise multiplication | +-------------------------+--------------------------------------------+ | :math:\lvert\mathcal{X | Cardinality (number of elements) of the | | }\rvert | set :math:\mathcal{X} | +-------------------------+--------------------------------------------+ | :math:\|\cdot\|_p | :math:L_p norm | +-------------------------+--------------------------------------------+ | :math:\|\cdot\| | :math:L_2 norm | +-------------------------+--------------------------------------------+ | :math:\sum | Series addition | +-------------------------+--------------------------------------------+ | :math:\prod | Series multiplication | +-------------------------+--------------------------------------------+ Functions --------- +---------------------+----------------------+ | Symbol | Type | +=====================+======================+ | :math:f(\cdot) | Function | +---------------------+----------------------+ | :math:\log(\cdot) | Natural logarithm | +---------------------+----------------------+ | :math:\exp(\cdot) | Exponential function | +---------------------+----------------------+ Derivatives and Gradients ------------------------- +-----------------------------------+-----------------------------------+ | Symbol | Type | +===================================+===================================+ | :math:\frac{dy}{dx} | Derivative of :math:y with | | | respect to :math:x | +-----------------------------------+-----------------------------------+ | :math:\partial_{x} {y} | Partial derivative of :math:y | | | with respect to :math:x | +-----------------------------------+-----------------------------------+ | :math:\nabla_{\mathbf{x}} y | Gradient of :math:y with | | | respect to :math:\mathbf{x} | +-----------------------------------+-----------------------------------+ Probability and Statistics -------------------------- +-----------------------------------+-----------------------------------+ | Symbol | Type | +===================================+===================================+ | :math:\Pr(\cdot) | Probability distribution | +-----------------------------------+-----------------------------------+ | :math:z \sim \Pr | Random variable :math:z obeys | | | the probability distribution | | | :math:\Pr | +-----------------------------------+-----------------------------------+ | :math:\Pr(x|y) | Conditional probability of | | | :math:x|y | +-----------------------------------+-----------------------------------+ | :math:{\mathbf{E}}_{x} [f(x)] | Expectation of :math:f with | | | respect to :math:x | +-----------------------------------+-----------------------------------+ Complexity ---------- +---------------------+-------------------------------------------------+ | Symbol | Type | +=====================+=================================================+ | :math:\mathcal{O} | Big O notation | +---------------------+-------------------------------------------------+ | :math:\mathcal{o} | Little o notation (grows much more slowly than) | +---------------------+-------------------------------------------------+