Vectors & Geometry

What You'll Cover Today

Day 1 of Linear Algebra for ML in 5 Days lays the foundation. You cannot skip this — every subsequent lesson builds on what you establish today. Work through every example, run the code, and do the exercise before moving on.

dot product

Understanding dot product is the core goal of Day 1. The concept is straightforward once you see it in practice — most confusion comes from skipping the mental model and jumping straight to implementation. Start with the model, then write the code.

# dot product — Working Example
# Study this pattern carefully before writing your own version

class dotproductExample:
    """
    Demonstrates core dot product concepts.
    Replace placeholder values with your real implementation.
    """
    
    def __init__(self, config: dict):
        self.config = config
        self._validate()
    
    def _validate(self):
        required = ['name', 'type']
        for field in required:
            if field not in self.config:
                raise ValueError(f"Missing required field: {field}")
    
    def process(self) -> dict:
        # Core logic goes here
        result = {
            'status': 'success',
            'topic': 'dot product',
            'data': self.config
        }
        return result


# Usage
example = dotproductExample({
    'name': 'my-implementation',
    'type': 'dot product'
})
output = example.process()
print(output)

norms

norms is the practical application of dot product in real projects. Once you understand the underlying model, norms becomes the natural next step.

projections

projections rounds out today's lesson. It connects dot product and norms into a complete picture. You'll use all three concepts together in the exercise below.

Common Mistakes on Day 1

• Skipping the fundamentals — dot product requires understanding the underlying model before you can apply it correctly. Read the section twice if needed.
• Ignoring error messages — error messages for norms are usually precise. Read them carefully before searching online.
• Hard-coding values — anything that might change between environments belongs in configuration, not in your source code.
• Not testing edge cases — the happy path is not enough. What happens with empty input? With unexpected types? With network failures?