Notation Preferences — Scientific Python

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Key	Meaning	Your Symbol	Default

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Global Notation — Scientific Python

Notation conventions used throughout the Scientific Python textbook. Mathematical notation is consistent with Books 1 and 2.

Linear Algebra (NumPy/SciPy)

Symbol	Meaning
$\mathbf{x}$	Vector (lowercase bold) — `np.ndarray` with `ndim=1`
$\mathbf{X}$	Matrix (uppercase bold) — `np.ndarray` with `ndim=2`
$(\cdot)^T, (\cdot)^H$	Transpose, conjugate transpose — `.T`, `.conj().T`
$\otimes$	Kronecker product — `np.kron()` or GPU-accelerated matvec
$\\|\mathbf{x}\\|_p$	$\ell_p$ norm — `np.linalg.norm(x, ord=p)`

Signal Processing

Symbol	Meaning
$\mathcal{F}\{x(t)\}$	Fourier transform — `np.fft.fft()` / `scipy.fft.fft()`
$*$	Convolution — `np.convolve()` / `scipy.signal.fftconvolve()`
$f_s$	Sampling frequency
$N_\\text{fft}$	FFT size

Optimization

Symbol	Meaning
$\\text{prox}_f(\\mathbf{x})$	Proximal operator — implemented as a Python function
$\\nabla f(\\mathbf{x})$	Gradient — `torch.autograd.grad()` or manual
$\\mathcal{S}_\\tau(\\mathbf{x})$	Soft-thresholding — `np.sign(x) * np.maximum(np.abs(x) - tau, 0)`

Deep Learning (PyTorch)

Symbol	Meaning
$f_\\theta$	Neural network — `nn.Module` with parameters $\theta$
$\\mathcal{L}(\\theta)$	Loss function — `loss.backward()` triggers autograd
$\\eta$	Learning rate
$B$	Batch size
$T$	Number of unrolling iterations or diffusion steps

Code Conventions

Symbol	Meaning
`snake_case`	Function and variable names
`CamelCase`	Class names
`UPPER_CASE`	Constants
`-> ReturnType`	Type hints on all public functions
`xp`	Array module variable (NumPy, CuPy, or PyTorch) for backend-agnostic code