Course Content
Introduction to AI and Machine Learning
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Overview of AI and ML – History and evolution of AI
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Differences between AI, ML, and Data Science
00:00
Types of Machine Learning : Supervised Learning
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Unsupervised Learning
00:00
Reinforcement Learning
00:00
Semi-supervised Learning
00:00
Applications of AI/ML
00:00
Mathematics for Machine Learning
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Linear Algebra : Vectors, Matrices, and Tensors
00:00
Eigenvalues and Eigenvectors
00:00
Singular Value Decomposition
00:00
Calculus : Differentiation and Integration
00:00
Partial Derivatives and Gradient Descent
00:00
Probability and Statistics : Probability Theory
00:00
Distributions (Normal, Binomial, etc.)
00:00
Bayes’ Theorem
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Optimization Techniques : Cost Function
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Optimization Algorithms
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Programming for AI/ML
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Introduction to Python : Python basics and libraries
00:00
Data Handling : Numpy, Pandas, Matplotlib
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Data Preprocessing and Cleaning
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Introduction to Jupyter Notebooks
00:00
Supervised Learning
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Linear Regression : Simple and Multiple Linear Regression
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Evaluation Metrics
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Classification Algorithms : Logistic Regression
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Decision Trees
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Support Vector Machines (SVM)
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k-Nearest Neighbors (k-NN)
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Model Evaluation : Confusion Matrix
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Precision, Recall, F1-Score
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ROC-AUC Curve
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Unsupervised Learning
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Clustering : k-Means Clustering
00:00
Hierarchical Clustering
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DBSCAN
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Dimensionality Reduction : Principal Component Analysis (PCA)
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t-SNE
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LDA
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Neural Networks and Deep Learning
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Introduction to Neural Networks : Perceptron Model
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Activation Functions
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Deep Learning : Multi-Layer Perceptrons (MLP)
00:00
Backpropagation
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Optimization Techniques (Adam, RMSProp)
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Convolutional Neural : Networks (CNNs) CNN Architecture
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Applications in Image Processing
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Reinforcement Learning
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Introduction to Reinforcement Learning : Markov Decision Processes (MDPs)
00:00
Q-Learning and Deep Q-Networks (DQN)
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Applications in Gaming and Robotics
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AI/ML Model Deployment
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Model Deployment Techniques : Flask, Django, FastAPI
00:00
Cloud Services : AWS, Google Cloud, Microsoft Azure
00:00
Monitoring and Scaling ML Models
00:00
AI/ML
About Lesson

Linear algebra is a branch of mathematics that deals with vectors, matrices, and tensors, which are essential tools in various fields such as physics, engineering, computer science, and machine learning.

Vectors

  • Definition: A vector is an object that has both magnitude and direction. It can be represented as an ordered list of numbers, which are its components.
  • Notation: Vectors are often denoted by bold letters (e.g., v) or by an arrow above the letter (e.g., v⃗vec{v}).
  • Operations:
    • Addition: The sum of two vectors is a vector obtained by adding their corresponding components.
    • Scalar Multiplication: A vector can be multiplied by a scalar (a real number), resulting in a vector whose magnitude is scaled by the scalar.
    • Dot Product: The dot product of two vectors is a scalar obtained by multiplying their corresponding components and summing the results.
    • Cross Product: The cross product of two vectors in three-dimensional space results in another vector perpendicular to the plane containing the original vectors.

Matrices

  • Definition: A matrix is a rectangular array of numbers arranged in rows and columns. It can be thought of as a collection of vectors.
  • Notation: Matrices are typically denoted by uppercase bold letters (e.g., A) or regular uppercase letters (e.g., AA).
  • Operations:
    • Addition: Matrices of the same size can be added by adding their corresponding elements.
    • Scalar Multiplication: Each element of a matrix can be multiplied by a scalar.
    • Matrix Multiplication: The product of two matrices is a new matrix obtained by taking the dot product of rows and columns.
    • Transpose: The transpose of a matrix is obtained by flipping it over its diagonal, converting rows into columns and vice versa.
    • Determinant: The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties related to the matrix.
    • Inverse: The inverse of a square matrix is another matrix that, when multiplied by the original matrix, yields the identity matrix.

Tensors

  • Definition: A tensor is a generalization of vectors and matrices. While vectors are first-order tensors (with one index), and matrices are second-order tensors (with two indices), tensors can have more indices (third-order, fourth-order, etc.).
  • Notation: Tensors are often denoted by boldface uppercase letters (e.g., T) or by regular uppercase letters with multiple indices (e.g., TijkT_{ijk}).
  • Operations:
    • Tensor Addition: Similar to vector and matrix addition, tensors of the same shape can be added element-wise.
    • Scalar Multiplication: Tensors can be multiplied by scalars, scaling each element of the tensor.
    • Tensor Contraction: This operation involves summing over pairs of indices of a tensor, reducing its order.
    • Outer Product: The outer product of two tensors results in a higher-order tensor.

Applications

  • Physics: Vectors are used to describe quantities such as force and velocity. Tensors are crucial in general relativity, where they represent the curvature of space-time.
  • Engineering: Matrices are used to solve systems of linear equations, model transformations, and perform stress-strain analysis.
  • Computer Science: Linear algebra underlies many algorithms in graphics, computer vision, and machine learning, particularly in the representation and manipulation of data.
  • Machine Learning: Tensors are used in deep learning frameworks to represent multidimensional data (e.g., images, videos, and complex datasets).
Linear Algebra : Vectors, Matrices, and Tensors
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