From 1be8d2ea75efdc9f1893ece8c436d0ca5efa6cfc Mon Sep 17 00:00:00 2001 From: medusa Date: Sun, 12 May 2024 18:12:04 +0000 Subject: [PATCH] Update tech_docs/math_objects_python.md --- tech_docs/math_objects_python.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/tech_docs/math_objects_python.md b/tech_docs/math_objects_python.md index ca20069..429fb3d 100644 --- a/tech_docs/math_objects_python.md +++ b/tech_docs/math_objects_python.md @@ -7,9 +7,9 @@ This document explains different types of mathematical objects and their applica A **scalar** is a single number, typically used in mathematics to represent a magnitude or quantity. In programming and data science, scalars are often used as individual data points or constants. ### Example -``` + $$ a = 3 $$ -``` + ### Python Libraries - **NumPy**: Used for handling numerical operations; scalars can be represented as `numpy.float64` or `numpy.int32`, etc. @@ -19,9 +19,9 @@ $$ a = 3 $$ A **vector** is an ordered array of numbers, which can represent direction and magnitude in space. Vectors are fundamental in physics for describing velocities and forces, in engineering for load distributions, and in machine learning for feature representation. ### Example -``` + $$ \mathbf{v} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} $$ -``` + ### Python Libraries - **NumPy**: Provides a powerful array structure that can be used to represent vectors. @@ -32,9 +32,9 @@ $$ \mathbf{v} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} $$ A **matrix** is a two-dimensional array of numbers used extensively in engineering, physics, computer science, and statistics. Matrices are crucial in solving systems of linear equations, transforming geometric data, and in algorithms for machine learning and artificial intelligence. ### Example -``` + $$ \mathbf{M} = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $$ -``` + ### Python Libraries - **NumPy**: Essential for creating and manipulating matrices. @@ -46,14 +46,14 @@ $$ \mathbf{M} = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $$ A **tensor** extends the concept of vectors and matrices to potentially higher dimensions. In the field of machine learning and neural networks, tensors are key structures, representing complex datasets and the parameters of the models themselves. ### Example -``` + $$ \mathcal{T} = \begin{bmatrix} \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} & \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \\ \begin{bmatrix} 9 & 10 \\ 11 & 12 \end{bmatrix} & \begin{bmatrix} 13 & 14 \\ 15 & 16 \end{bmatrix} \end{bmatrix} $$ -``` + ### Python Libraries - **TensorFlow**: A library designed specifically for working with tensors in neural networks.