Zen Math
Zen Math
  • Видео 13
  • Просмотров 626
Linear Algebra for Data Science: Foundations and Projects with Python and MATLAB
What is Linear Algebra? A Beginner’s Guide to Its Importance in Data Science and AI
Dive into the fascinating world of linear algebra, the foundation of modern data science, machine learning, and artificial intelligence. In this lesson, we’ll explore:
The core concepts of linear algebra: linear equations, transformations, vectors, and matrices.
Real-world applications like dimensionality reduction, neural networks, and image transformations.
How these mathematical tools power everything from recommendation systems to AI-driven innovations.
Whether you’re just starting or looking to solidify your understanding, this video provides a beginner-friendly introduction with engaging visuals and clear...
Просмотров: 30

Видео

Mastering the Dot Product The Foundation of Machine Learning and AI7:29Mastering the Dot Product The Foundation of Machine Learning and AI
Mastering the Dot Product The Foundation of Machine Learning and AI
Просмотров 1719 часов назад
In this video, we explore the fundamental concept of the dot product and its wide-ranging applications. Starting from its mathematical definition to its geometric interpretation, we break down how the dot product is used in real-world scenarios. Discover how the dot product forms the foundation of machine learning techniques like linear regression, neural networks, and recommendation systems. W...
Understanding Curl: A Key Concept in Physics-Inspired Machine Learning and Vector Analysis7:58Understanding Curl: A Key Concept in Physics-Inspired Machine Learning and Vector Analysis
Understanding Curl: A Key Concept in Physics-Inspired Machine Learning and Vector Analysis
Просмотров 4621 час назад
In this video, we explore the fascinating concept of curl in vector calculus and its applications in 3D spaces. We start with a clear understanding of curl in 2D and extend it to 3D vector fields, explaining how curl measures the rotational tendencies of a field at every point. Using a practical example, we calculate the curl of a 3D vector field step by step, illustrating the process with visu...
Mastering Gradients in Machine Learning: Concepts, Visualization, and Python Implementation5:08Mastering Gradients in Machine Learning: Concepts, Visualization, and Python Implementation
Mastering Gradients in Machine Learning: Concepts, Visualization, and Python Implementation
Просмотров 96День назад
In this tutorial, we dive deep into the concept of gradients, a foundational tool in machine learning and optimization. Learn how gradients are used in loss function minimization, gradient descent, and optimization algorithms. We’ll explore: What gradients are and their role in machine learning. How to compute gradients mathematically and programmatically. Visualizing gradient fields and gradie...
Understanding Hessians: Optimize Machine Learning and Neural Networks5:39Understanding Hessians: Optimize Machine Learning and Neural Networks
Understanding Hessians: Optimize Machine Learning and Neural Networks
Просмотров 38День назад
Learn how to compute and apply the Hessian matrix in neural networks using TensorFlow! This tutorial explains the concept of the Hessian matrix, its role in optimization, and how to implement it for a loss function in a simple neural network. Perfect for anyone interested in advanced machine learning techniques and optimization insights.
Understanding Jacobians: A Key Tool for Machine Learning and Neural Networks4:09Understanding Jacobians: A Key Tool for Machine Learning and Neural Networks
Understanding Jacobians: A Key Tool for Machine Learning and Neural Networks
Просмотров 44День назад
Learn how Jacobians play a critical role in machine learning and neural networks. In this video, we break down what Jacobians are, their mathematical foundations, and how they help analyze the relationship between inputs and outputs in neural networks. Plus, see a practical example of computing the Jacobian matrix in TensorFlow. Perfect for anyone looking to deepen their understanding of key co...
Orthogonality of Eigenvectors of Hermitian Matrices2:20Orthogonality of Eigenvectors of Hermitian Matrices
Orthogonality of Eigenvectors of Hermitian Matrices
Просмотров 21День назад
This video explains the theorem stating that for any Hermitian matrix, eigenvectors corresponding to distinct eigenvalues are orthogonal. We provide a step-by-step proof using the properties of Hermitian matrices, eigenvalues, and inner products. Ideal for students and professionals seeking a deeper understanding of linear algebra concepts.
Orthogonality of Eigenvectors of Symmetric Matrices2:17Orthogonality of Eigenvectors of Symmetric Matrices
Orthogonality of Eigenvectors of Symmetric Matrices
Просмотров 2214 дней назад
In this video, we explore the proof that the eigenvectors of symmetric matrices are always orthogonal. Follow a clear, step-by-step explanation of this fundamental result in linear algebra. Perfect for students and math enthusiasts aiming to understand the unique properties of symmetric matrices.
Eigenvalues of Hermitian Matrices2:56Eigenvalues of Hermitian Matrices
Eigenvalues of Hermitian Matrices
Просмотров 1714 дней назад
In this video, we explore the proof that Hermitian matrices always have real eigenvalues. Learn step-by-step how the properties of Hermitian matrices lead to this important result in linear algebra. Ideal for students and enthusiasts looking to deepen their understanding of matrix theory.
Hermitian Matrices1:39Hermitian Matrices
Hermitian Matrices
Просмотров 6414 дней назад
In this video, we dive into the concept of Hermitian matrices, a fundamental topic in linear algebra. We explain the defining property of Hermitian matrices, where the matrix is equal to its conjugate transpose. You’ll learn how the diagonal elements must be real numbers and how the off-diagonal elements are complex conjugates of each other. Using clear explanations and examples, this video bre...
Eigenvalues of Symmetric Matrices1:38Eigenvalues of Symmetric Matrices
Eigenvalues of Symmetric Matrices
Просмотров 2614 дней назад
Proof of why symmetric matrices have real eigenvalues, a fundamental result in linear algebra with applications in data science, physics, and machine learning. This video explains the step-by-step reasoning behind the theorem, breaking down key concepts with clear mathematical notation and narration. We explore the eigenvalue equation, the role of symmetry, and how it guarantees real eigenvalue...
Fourier Transform2:30Fourier Transform
Fourier Transform
Просмотров 9314 дней назад
This video breaks down how the Fourier Transform converts signals from the time domain to the frequency domain, revealing the hidden frequency components within any signal. Using a sine wave as an example, we explore the math step by step to show how the Fourier Transform decomposes signals into their fundamental frequencies. Understand why the Fourier Transform produces spikes in the frequency...
Fourier Transform in Speech Recognition5:08Fourier Transform in Speech Recognition
Fourier Transform in Speech Recognition
Просмотров 13814 дней назад
In this video, we explore the Fourier Transform and its applications in breaking down complex audio signals into their frequency components. Learn how to record audio, generate spectrograms, and extract Mel-Frequency Cepstral Coefficients (MFCCs) - key features for machine learning applications like speech recognition, sentiment analysis, and audio classification. 🚀 What's Included: Step-by-ste...