The Jacobian Matrix - Explained

Learn the Jacobian matrix in a simple and intuitive way, starting from basic calculus and derivatives, moving through partial derivatives in multivariable functions, and finally seeing how Jacobians are used in data science and neural networks. This video covers the fundamentals of the Jacobian matrix, its structure, and why it’s so important for machine learning, deep learning, and gradient computation. *Related Videos* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Bayesian Optimization: https://youtu.be/Kq6_kzlwSUQ Hyperparameters Tuning: Grid Search vs Random Search: https://youtu.be/G-fXV-o9QV8 The Kernel Trick: https://youtu.be/N_RQj4OL1mg Cross-Entropy - Explained: https://youtu.be/Fv98vtitmiA Dropout - Explained: https://youtu.be/FDF_Q3_98GQ Overfitting vs Underfitting: https://youtu.be/B9rhzg6_LLw Why Models Overfit and Underfit - The Bias Variance Trade-off: https://youtu.be/5mbX6ITznHk Least Squares vs Maximum Likelihood: https://youtu.be/WCP98USBZ0w XGBoost Explained in Under 3 Minutes: https://youtu.be/33fGfuleXw0 *Contents* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 00:00 - Intro 00:13 - Single variable function 00:34 - Multivariable function 01:17 - Multiple functions of multiple variables 01:49 - The Jacobian Matrix 02:39 - Application: Neural Networks 04:28 - Outro *Follow Me* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🐦 Twitter: @datamlistic https://twitter.com/datamlistic 📸 Instagram: @datamlistic https://www.instagram.com/datamlistic 📱 TikTok: @datamlistic https://www.tiktok.com/@datamlistic 👔 Linkedin: https://www.linkedin.com/company/datamlistic *Channel Support* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ The best way to support the channel is to share the content. ;) If you'd like to also support the channel financially, donating the price of a coffee is always warmly welcomed! (completely optional and voluntary) ► Patreon: https://www.patreon.com/datamlistic ► Bitcoin (BTC): 3C6Pkzyb5CjAUYrJxmpCaaNPVRgRVxxyTq ► Ethereum (ETH): 0x9Ac4eB94386C3e02b96599C05B7a8C71773c9281 ► Cardano (ADA): addr1v95rfxlslfzkvd8sr3exkh7st4qmgj4ywf5zcaxgqgdyunsj5juw5 ► Tether (USDT): 0xeC261d9b2EE4B6997a6a424067af165BAA4afE1a #jacobian #calculus #machinelearning #deeplearning #neuralnetworks