Vector Representation & Components

Linear Algebra for Machine Learning · Axiom Academy

Representing a House as a Vector Worked example: turning a real object into mathematical data We want to represent a house using numerical features Consider a house with these characteristics: Extract relevant numerical features We've chosen three features to describe our house: Feature 1: Square footage (continuous, in units) Order matters! Create a consistent ordering We decide: [Square footage, Bedrooms, Price] This ordering must be consistent across all houses we represent. Substitute the values in order: This is a 3-dimensional vector representing our house as a point in 3D feature space! Representing multiple houses creates a dataset Using the same feature ordering, we can represent an entire dataset: Question 1: Vector Representation If we represent a different house with 1800 sqft, 3 bedrooms, and 320,000 price, what is its vector representation? Question 2: Why Vectors Matter Why is it important that a vector is an ORDERED collection (not just any collection)? By representing objects as vectors, we translate real-world problems into mathematics. Once data is vectorized, we can use powerful mathematical operations to: • Measure distances between objects (similarity) • Find patterns in large datasets • Train machine learning models • Perform comparisons and predictions

This is the written version of the interactive lesson above. See the full Linear Algebra for Machine Learning course.