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Linear Algebrafirst principles.

MATH FOR AI • FROM ZERO TO MODELS.

Chapter-by-chapter theory notes, step-by-step textbook exercises, video lectures, and SLO-aligned board examination prep for Linear Algebra (Math for AI).

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Syllabus

Curriculum Syllabus

Course chapter sequence roadmap and learning outcomes.

Linear Algebra (Math for AI)

1. Vectors

1.1 What Is a Vector?
1.2 Vector Operations
1.3 Dot Product

2. Matrices

2.1 Matrices & Notation
2.2 Matrix Operations
2.3 Matrices as Transformations
2.4 Matrix Inverse

3. Systems of Linear Equations

3.1 Linear Systems & Their Geometry
3.2 Gaussian Elimination
3.3 Particular & General Solutions

4. Vector Spaces and Basis

4.1 Groups & Vector Spaces
4.2 Subspaces
4.3 Linear Independence
4.4 Basis, Dimension & Rank

5. Linear Mappings and Affine Spaces

5.1 Linear Mappings
5.2 Kernel & Image
5.3 Change of Basis
5.4 Affine Spaces & Maps

6. Norms and Inner Products

6.1 Norms
6.2 Inner Products
6.3 Lengths & Distances

7. Angles and Orthogonality

7.1 Angles
7.2 Orthogonality
7.3 Orthogonal Complements & Function Spaces

8. Projections and Rotations

8.1 Projection onto a Line
8.2 Projection onto a Subspace
8.3 Least Squares & Pseudo-Inverse
8.4 Gram–Schmidt
8.5 Rotations

9. Determinant and Trace

9.1 Determinant
9.2 Trace

10. Eigenvalues and Eigendecomposition

10.1 Eigenvalues & Eigenvectors
10.2 Eigendecomposition
10.3 Cholesky Decomposition

11. Singular Value Decomposition

11.1 The SVD
11.2 Low-Rank Approximation
11.3 Matrix Phylogeny
INTERACTIVE LAB • 18 STEM WORKSTATIONS

Bridge High-School Science to Computational AI

Connect textbook physics, mathematics, and computing to real-world artificial intelligence models and symbolic solvers.

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