Orthogonality and the Four Fundamental Subspaces
A thorough analysis of how orthogonality is intertwined with the core concepts of linear algebra.
Subtopics:
- Understanding orthogonality: A conceptual overview.
- Orthogonal relations among the four subspaces:
- Rowspace & Null Space
- Columnspace & Left Null Space
- Implications of orthogonality in linear algebra and beyond.
Projections: Casting Shadows in Vector Spaces
Exploring how the concept of projections is crucial in various mathematical and practical applications.
Topics Covered:
- The geometric essence of projection: Intuition and significance.
- Mathematical formulation of projections.
- Applications in least squares, regression, and more.
The Normal Vector: More Than Just Perpendicular
An in-depth look into the world of normal vectors and their multifaceted significance in mathematics and physics.
Key Insights:
- Defining the normal vector: What makes it “normal”?
- Importance in defining planes, surfaces, and boundaries.
- Relationship with orthogonality and projections.
