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Free Certificate
Linear Algebra for Analysis
Master the essentials of linear algebra in this free course! Learn about vectors, matrices, transformations, eigenvalues, and eigenvectors to enhance your analytics skills and problem-solving capabilities.
5 hours of learning
Data Manipulation
Vectors
Problem Solving
Key Highlights Of This Linear Algebra Free Course
What You Will Learn
Vectors & Vector Spaces
Start your linear algebra journey with the basics of vectors and their properties, essential for understanding various mathematical and scientific concepts.
Topics Covered
- The Foundation of Linear Algebra
Vectors are fundamental in linear algebra, serving as building blocks for more complex concepts. Understanding their properties is essential for anyone venturing into fields like data science, physics, and engineering. This section will establish the critical role of vectors in representing quantities with magnitude and direction, and how they form the foundation for vector spaces and transformations. - Vector Operations
Learn the core operations that can be performed with vectors, such as addition, scalar multiplication, and dot product. These operations allow vectors to interact with each other in meaningful ways, essential for solving systems of equations and manipulating data in various applications like machine learning algorithms. - Vector Spaces
Vector spaces are collections of vectors that follow certain rules of addition and scalar multiplication. This subtopic explains how vector spaces enable the formulation of systems and solutions in higher-dimensional spaces. You'll also explore key concepts like span, basis, and dimension, which help in understanding complex transformations.
Linear Transformation & Matrices
This session will explore matrices and their role in linear transformations, laying the groundwork for more advanced topics in data science and machine learning.
Topics Covered
- Importance of Linear Transformation
Linear transformations map vectors from one vector space to another. This section emphasizes how these transformations are represented using matrices. You will understand how linear transformations preserve the structure of vector spaces, which is crucial for solving equations and simplifying complex systems, especially in data transformations. - Matrices
Matrices are arrays of numbers arranged in rows and columns. They serve as a tool to represent linear transformations, and this subtopic will teach you how to work with matrices. You'll cover matrix multiplication, addition, and how matrices are used in various fields such as computer graphics, statistics, and optimization. - Matrix Operations
Learn the core matrix operations: addition, multiplication, and inversion. These operations are essential for solving linear equations, performing data transformations, and computing systems in fields like machine learning and computer vision. You'll understand the importance of matrix operations in manipulating data for various applications. - Determinants
Determinants provide useful information about matrices, such as whether a matrix has an inverse and its geometric interpretation. You'll learn how to calculate and interpret determinants to assess the solvability of linear systems and their implications in solving real-world problems. - Linear Independence
This subtopic explains linear independence, a key concept in determining whether a set of vectors forms a basis for a vector space. It also explores how linear independence relates to the solvability of systems of linear equations and how it is used to simplify and analyze data.
Eigenvalues & Eigenvectors
This session will introduce eigenvectors and eigenvalues, exploring how they are calculated and their relevance to data analysis techniques like Principal Component Analysis (PCA).
Topics Covered
- Eigenvectors: A Special Type of Vector
Eigenvectors are vectors that remain unchanged in direction when a linear transformation is applied, though their magnitude may change. This subtopic introduces the concept of eigenvectors and how they help in simplifying complex problems in data analysis, computer science, and physics by reducing the dimensions of data. - Calculation of Eigenvalues
Eigenvalues are scalar values that indicate how much an eigenvector is stretched or shrunk during a linear transformation. You'll learn how to compute eigenvalues using the determinant of a matrix and understand their significance in identifying system behaviors, such as stability in dynamic systems. - Applications
Eigenvalues and eigenvectors play a crucial role in techniques like Principal Component Analysis (PCA), which is widely used in data science for dimensionality reduction. This section explores how these concepts are used in real-world applications, such as image compression, machine learning, and network analysis.
Linear Algebra Free Course Certification
Earn and Share Your Certificate
Official & Verifiable
Receive a signed and verifiable e-certificate from upGrad upon successfully completing the course.
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