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# Statistics and linear algebra for machine learning

## Statistics:

### 1. Descriptive Statistics:

**Mean, Median, Mode:** Measures of central tendency help summarize and understand the distribution of data.
**Standard Deviation, Variance: **Measures of dispersion provide insights into the spread of data points.

### 2. Inferential Statistics:

**Probability Distributions: **Understanding probability distributions is essential for modeling uncertainties in data.
**Hypothesis Testing: **Used to make inferences about population parameters based on sample data.

### 3. Statistical Learning:

**Regression Analysis:** Modeling the relationship between variables.
**Classification: **Assigning labels or categories to data points based on statistical models.

### 4. Sampling Techniques:

**Random Sampling: **Ensures representative subsets for training and testing data.
**Bootstrapping:** Resampling technique used for estimating the distribution of a statistic.

## Linear Algebra:

### 1. Vectors and Matrices:

**Vectors:** Representing data points and features.
**Matrices: **Used for transformations, such as feature scaling and data manipulation.

### 2. Matrix Operations:

**Addition, Subtraction, Multiplication: **Fundamental operations for manipulating data and parameters.
**Transpose:** Flipping rows and columns, often used in calculations.

### 3. Eigenvalues and Eigenvectors:

**Principal Component Analysis (PCA): **Dimensionality reduction technique.
**Spectral Clustering:** Clustering algorithm based on eigenvectors.

### 4. Matrix Decompositions:

**Singular Value Decomposition (SVD):** Used in latent semantic analysis and collaborative filtering.
**LU Decomposition: **Solving linear equations efficiently.

### 5. Linear Transformations:

**Linear Maps: **Used in linear regression and neural networks.
**Affine Transformations: **Translation and scaling operations.

### 6. Linear Independence and Rank:

**Determining Rank:** Assessing the number of linearly independent columns or rows in a matrix.
**Rank-Nullity Theorem: **Essential in understanding the dimensionality of the solution space.