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Master the Math for Data Science

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Linear algebra

Prob and stats

Machine learning

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

1. Basics of statistics

Population, samples and sampling techniques

Measures of central tendency

Measures of spread

Quantiles, quartiles and percentiles

Histogram

Box-plot diagrams

2. Basics of probability theory

Basics of set theory and Venn diagrams

Counting with permutations

Counting with combinations

Sample space, events and probability axioms

Conditional probability

Multiplication and addition rule

Law of total probability

Bayes' theorem

3. Random variables

Random variables

Expected value

Properties of expected value

Variance

Properties of variance

Covariance

Correlation

4. Point estimation

Sample estimators

Sample mean

Sample variance

Sample covariance

Sample correlation

Unbiased estimator

Mean squared error

Sampling distribution of the sample mean

5. Discrete probability distributions

Probability mass function

Binomial distribution

Geometric distribution

Negative binomial distribution

Hypergeometric distribution

Poisson distribution

1. ML models

Simple linear regression

Logistic regression

k-means clustering

Hierarchical clustering

DBSCAN

Naive bayes

Decision trees

k-nearest neighbors

Perceptrons

2. Feature engineering

Feature scaling

Log transformation

Text vectorization

Grid search

Random search

Principal component analysis

3. Optimization

Gradient descent

4. Model evaluation

Confusion matrix

ROC curve

Cross validation

Mean squared error

Mean absolute error

Root mean squared error

r-squared

We're not just another math course

Most DS courses either:

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

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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

Most DS courses either gloss over the details or throw around complex math equations without explanation. We achieve the best of both worlds by deep-diving into the technical details while developing your intuition with:

format_list_numbered

Step-by-step proofs

local_library

Insightful diagrams

layers

Simple examples

Elevate your learning experience

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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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