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Learn the Foundational Topics for Data Science

Academic rigor of an undergrad textbook

but with

but with

**less bloat**and**more intuition**Web Platform Subscription

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Here's a sneak-peek of our ebooks

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Linear algebra

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20

guides

article

20

pages

casino

Prob and Stats

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20

guides

article

20

pages

smart_toy

Machine learning

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20

guides

article

20

pages

function

Misc math topics

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20

guides

article

20

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Dagster

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20

guides

article

20

pages

Pandas

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20

API

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20

pages

NumPy

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20

API

article

20

pages

PySpark

code

20

API

article

20

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This ebook is targeted for those looking to build a strong foundation in linear algebra for data science. The ebook has no prerequisite but takes you to advanced undergraduate level - all that's needed for data science. Every theorem comes with a full proof, supplemented with intuitive explanations and diagrams.

Download ebook (preview)

1. Vectors

Introduction

Position vectors

Planes

Dot product

2. Matrices

Introduction

Transpose of matrices

Trace of matrices

Invertible matrices

Elementary matrices

3. Linear equations

System of linear equations

Gaussian Elimination

Pivot positions and columns

Linear dependence and independence

Linear transformation

4. Matrix determinant

Introduction

Determinant of elementary matrices

Invertibility, multiplicative and transpose properties of determinants

Laplace expansion theorem

Cramer's rule and finding inverse matrix using determinants

Geometric interpretation

5. Vector space

Subspace

Relationship between pivots and linear dependence

Spanning Set of a vector space

Basis vectors

Constructing a basis for a vector space

Null space

Column space

Rank and nullity

6. Special matrices

Symmetric matrices

Triangular matrices

Diagonal matrices

Block matrices

LU factorization

7. Eigenvalues and Eigenvectors

Introduction

Basic properties

Eigenspace and eigenbasis

Similar matrices

Diagonalization

Algebraic and geometric multiplicity

8. Orthogonality

Orthogonal projections

Orthonormal sets and bases

Orthogonal complement

Orthogonal matrices

Least squares

Gram-Schmidt process

9. Matrix decomposition

QR decomposition

Orthogonal diagonalization

Positive definite matrices

Schur's triangulation theorem

Cholesky decomposition

Singular value decomposition

Data compression using singular value decomposition

We're not just another math course

Most DS courses either:

- gloss over the technical details, or
- throw complex math equations without explanation

We achieve the best of worlds by deep-diving into the technicality while developing your intuition with:

format_list_numberedstep-by-step proofs

diagrams

simple examples

Theorem.

# Product of block matrices (3)

Suppose we have two block matrices where each matrix is composed of four sub-matrices. The product of the two block matrices is:

Note that the shape of the matrices must match for the matrix product to be valid. For instance, the number of columns of

We're not just another math course

Our courses offer a unique blend of technicality and intuition, providing you with a deep and satisfying understanding of data science.

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Step-by-step proofs

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Insightful diagrams

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Simple examples

Elevate your learning experience

priorityRigorous content

We dive deeper into the technical details than any other online course.

boltEvery theorem is proven

We offer an intuitive step-by-step proof for every theorem - no exceptions!

mediationBeginner-friendly

We go from basic high school to advanced undergraduate mathematics.

boltBlazing-fast search

Find definitions, theorems and topics using our search engine without navigating to a new page!

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Visualize the connections between the math topics. Track your learning progress and complete the map!

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Meet the team

Obtained a bachelors at UTokyo, a masters of DS at HKU, and now working as a MLE. I'm mainly in charge of the tech-side of SkyTowner, and I love writing articles about data science!

Graduated from UTokyo, and now working in the finance industry. I consider myself a citizen developer and write about topics as they come!

Eva

Graduated from HKUST, and now brushing up my programming skills. I enjoy documenting my learning process on SkyTowner!

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FAQ

Why should I pay if other resources are free?

We emphasize on the quality of your education - you'll learn much faster and deeper with our guides than you would by reading through some blog post.

I'm not good at math. Is SkyTowner right for me?

Our guides are beginner-friendly and we have lots of diagrams and examples to help you grasp abstract concepts! Also, we'll do our best to help if you get stuck!

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All content is human-generated - even the API documentations!