Calculus & Linear Algebra for Machine Learning from Scratch

This lecture introduces the matrix as a rectangular arrangement of numbers, with real-life examples from two factories’ revenue and workers, and defines rows, columns, and dimensions such as 2x3.

Learn how to locate elements in a matrix using row and column indices, and apply the E R C notation to identify coordinates.

Learn how to compute the transpose of a matrix by turning its rows into columns, using the superscript T notation with examples like A, B, and C.

Explore three fundamental matrix types: zero, diagonal, and identity, noting main-diagonal values and zero off-diagonal entries. Analyze 3x3 and 4x4 examples to distinguish their structure and conditions for identity matrices.

Add and subtract matrices by adding or subtracting corresponding elements in matrices of the same dimension, using a 2x2 example to illustrate element-wise operations and dimension compatibility.

Learn how to perform scalar multiplication of matrices by multiplying every element by a scalar, illustrated with examples like 5 times a matrix and 3 times another matrix.

Learn that a vector is a matrix with only one row or one column, illustrated by examples like V and B, while a 2x2 matrix is not a vector.

Learn how to multiply matrices by aligning columns and rows, determine when multiplication is possible, and compute results using vector and matrix examples.

Compute the product of matrices a and b using the standard procedure to form the resultant matrix, following column-by-column multiplication and simplification.

Discover how the determinant, a fundamental property of square matrices, is calculated for 2x2 matrices using ad minus bc, with examples; higher-order determinants are not covered.

Compute a matrix inverse by ensuring a nonzero determinant, swap the diagonal elements, negate the off-diagonal elements, and divide by the determinant to yield the identity when multiplied.

Explore eigenvalues and eigenvectors of a matrix by solving det(A - λI)=0, finding λ=2 and 5, and deriving eigenvectors such as [1, -1] and [1, 2].

Explore how machine learning powers real-world applications like virtual assistants, recommendations, spam detection, and price predictions. Learn how data and training tune model parameters to enable accurate predictions.

Learn how linear regression uses car features like top speed and price data to predict optimal car pricing, then train parameters to minimize error and improve pricing decisions.

Learn how to train a linear regression model with the normal equation, forming a feature matrix with ones and computing theta hat as (X^T X)^{-1} X^T y.

Master gradient descent to minimize the loss function and obtain optimal regression parameters, using learning rate steps to align predictions with actual values and reduce squared errors.

Learn to load a CSV dataset in Google Colab by mounting Google Drive, importing a data library, and previewing the first rows to set up a price-prediction ML project.

Organize the data by splitting it into two data frames: features X (gold amount and making charges) and the response price for training.

Split the data into training and test sets using X and Y, with test_size 0.2 and random_state, then train on the training set and evaluate predictions on the test set.

Import a model, set a random state, and train a random forest on your dataset by fitting the model to the training data.

Evaluate the trained model by comparing its predictions on the X test dataset to the actual values, confirming accuracy for future predictions.

Format input data as a dataframe in a specific structure with features like gold grams and making charges, then use a machine learning model to predict the price.