₹0 for students · Certificate · Beginner

Linear Algebra for Computing

4 mini courses, 15 lessons: vectors, matrices, solving systems, and eigenvectors in search and ML

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15 lessons · ~3 hours · 30-question final exam · pass mark 70%

About the course

What you’ll learn

The maths behind graphics, search engines, recommendation systems and machine learning, explained with pictures and code instead of long proofs. Learn vectors and similarity, matrices as transformations, solving systems of equations, and eigenvectors, PCA and SVD, and see how Google ranked pages and how embeddings power AI search. Every idea is coded in plain Python. Pass every lesson quiz and the final exam to earn a verifiable certificate.

VectorsMatricesLinear systemsEigenvectorsMaths for ML

Part of the career tracks: Machine Learning Engineer, GenAI and LLM Builder, Computer Science Foundations

How the certificate works

  1. Read each lesson’s study guide, then the full lesson and any notebooks or exercises.
  2. Pass every lesson quiz with 70% or more.
  3. Pass the final exam: 30 questions in 45 minutes.
  4. Get a certificate with a public verification link, and add it to LinkedIn.

Syllabus

15 lessons in 4 mini courses

Each mini course takes about an hour. Already know one? Test out in the app and skip it.

1. Vectors

Add, scale and compare vectors, and measure similarity with the dot product.

1
Vectors
10 min · A vector is an ordered list of numbers; its length is the dimension.
2
Dot Product, Length and Angle
12 min · Dot product: multiply matching entries and add.
3
Cosine Similarity and Embeddings
10 min · Cosine similarity = u · v / (|u||v|), from −1 to 1.

2. Matrices

Multiply matrices and use them as transformations.

4
Matrices and Matrix–Vector Products
10 min · A matrix is m rows × n columns of numbers.
5
Matrix Multiplication
12 min · (m × n)(n × p) = m × p; inner sizes must match.
6
Matrices as Transformations
10 min · A matrix transforms every point of space.
7
Identity, Inverse and Transpose
10 min · The identity I leaves every vector unchanged.

3. Solving systems

Solve linear systems and reason about rank, independence and determinants.

8
Linear Systems and Gaussian Elimination
12 min · Linear equations can be written Ax = b.
9
Span, Independence and Rank
12 min · Span: everything reachable by linear combinations.
10
Determinants
10 min · The determinant is how much a transformation scales area or volume.

4. Eigenvectors and applications

Explain eigenvectors, PageRank, PCA, SVD and least squares.

11
Eigenvalues and Eigenvectors
12 min · An eigenvector is only stretched by A: Av = λv.
12
PageRank: Eigenvectors in Search
10 min · PageRank: a page is important if important pages link to it.
13
PCA: Reducing Dimensions
12 min · PCA finds directions where data varies most.
14
SVD: Compression and Recommendations
12 min · SVD: A = UΣVᵀ, rotate, stretch, rotate.
15
Least Squares and Linear Regression
10 min · With more equations than unknowns, least squares minimises the squared error.

Written by Vikosha. Lessons, questions and exercises are original. Licence: Original Vikosha course..