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Learn the Foundational Topics for Data Science
Academic rigor of an undergrad textbook
but with less bloat and more intuition
but with less bloat and more intuition
Web Platform Subscription
$89.9 per year
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Get an e-book for only $29.9 $19.9
(limited-time beta discount)
Here's a sneak-peek of our ebooks
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Linear algebra
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20
guides
article
20
pages
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Prob and Stats
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20
guides
article
20
pages
smart_toy
Machine learning
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20
guides
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20
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function
Misc math topics
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20
guides
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20
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Dagster
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20
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article
20
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Pandas
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20
API
article
20
pages
NumPy
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article
20
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PySpark
code
20
API
article
20
pages
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!
mapInteractive map
Visualize the connections between the math topics. Track your learning progress and complete the map!
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Find definitions, theorems and topics using our search engine without navigating to a new page!
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Show linked definitions, theorems and examples on the left side panel for reference!
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!
Subscription
$69.9 per year
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Digital e-book
$19.9 per book
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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!
Is your content AI-generated?
All content is human-generated - even the API documentations!
