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# Linear Algebra

Linear Algebra

RELATED RECENT PLACEMENTS

## Syllabus

This course is full of best-in-class content by leading faculty and industry experts in the form of videos and projects

## Course Overview

• The course starts with a basic introduction to linear systems and their graphical interpretations.
• It explains some important concepts about vector spaces, and it deals with a few concepts from statistics, such as least squares methods and linear regressions.
• It provides some knowledge on curve fitting and an introduction to ordinary and partial differential equations.
• It provides detailed ideas related to state space methods in control theory, followed by crucial ideas on spectral graph theory.
• Overall, it covers the linear algebra aspects of computer vision, control theory, and graphical modelling.

### Course Syllabus

On a daily basis we talk to companies in the likes of Tata Elxsi and Mahindra to fine tune our curriculum.

Week 1 - Linear Equations and Matrix Algebra

• System of Linear Equations
• Consistent and Inconsistent Systems
• Matrix Formations
• Types of Matrices
• Sparse Matrix
• Matrix Arithmetic
• Determinants
• Matrix Inversions

Week 2 - Matrix Operations and Vectors

• Matrix Operations
• Gaussian Elimination
• Row Reduced Echelon Form
• Gauss-Jordan for Inverse
• Introduction to Vectors and Vector Arithmetic

Week 3 - Vector Spaces, Subspaces, Introduction to Bases

• Introduction to Vector Spaces
• Vector Operations
• Subspaces
• Linear Combinations
• Linearly Dependent and Independent Vectors
• Geometric Interpretations

Week 4 - Bases and Dimensions, Row-Equivalence

• A Span of a Set of Vectors
• Basis of a Vector Space
• Dimension of a Vector Space
• Row-Equivalence Revisited
• Introduction to Transformations

Week 5 - Linear Transformations

• Linear Transformations of Vector Spaces
• Domain and Range
• Null Space
• Rank and Nullity
• Rank-Nullity Theorem
• Representation of Transformation Matrices
• Rotation, Reflection, and Translation

Week 6 - Orthogonal Projection, Orthonormal Basis, Eigenvalues and Eigenvectors

• Orthogonal Projection and Orthonormal Basis
• Euclidean Transformation
• Introduction to Polynomials
• Characteristic Polynomials
• Eigenvalues and Eigenvectors, Eigenspaces

Week 7 - Similarity Transformation and Diagonalization, SVD, PCA, LSM

• Similarity Transformations
• Diagonal Matrices
• Diagonalizations
• Eigendecomposition
• Singular Value Decomposition
• Principal Component Analysis
• Least Square Method

Week 8 - Partial Differential Equations, Taylor Series, Fourier and Laplace Transformations

• Introduction to Partial Differential Equations and Solving Methods
• Taylor Series Expansion
• Fourier and Laplace Transformations

Week 9 - State Space Models, Digital Control Systems, Realization Theory

• Introduction to State-Space Models
• Introduction to Digital Control System and its Structure
• The z-transformation
• Realizations of State-Space Models

Week 10 - Introduction to Spectral Graph Theory

• Introduction to Graphs and their Properties
• Adjacency Matrix and Related Theorems
• Corollaries and Observations
• The Spectrum of a Graph

Week 11 - Spectral Graph Theory

• Positive Semi-Definite and Positive Definite Matrices
• Line Graphs and Associated Incidence Matrices
• A Subgraph of a Graph and their Adjacency Matrices
• A Spectrum of Subgraphs Compared to the Graphs

Week 12 - Linear Algebra Summary and Research Ideas

• Revision of All the Previously Discussed Ideas
• Applications of Matrices and Linear Algebra in Predicting Sports Ranking
• Ongoing Research Works

Our courses have been designed by industry experts to help students achieve their dream careers

### Industry Projects

Our projects are designed by experts in the industry to reflect industry standards. By working through our projects, Learners will gain a practical understanding of what they will take on at a larger-scale in the industry. In total, there are 2 Projects that are available in this program.

Camera Calibration of a Checkerboard, Using Linear Algebra

In this project, the learners have to perform a camera calibration of grids with the implementation of linear algebra and also have to write and compare different codes to perform the tasks and find the optimal runtime and complexity of execution.

An Approach to Networks and Small World Models Using Graph Theory

In this project, the learners will apply the knowledge of graph theory and linear algebra by extending them to real-world problems, modelling them, and implementing them in a challenging algebraic environment.

Our courses have been designed by industry experts to help students achieve their dream careers

### Ratings & Reviews by Learners

Skill-Lync has received honest feedback from our learners around the globe.

4.8

#### Flexible Pricing

Talk to our career counsellors to get flexible payment options.

INR 40,000

Inclusive of all charges

Become job ready with our comprehensive industry focused curriculum for freshers & early career professionals

• 5 Years Accessto Skill-Lync’s Learning Management System (LMS)

• Personalized Pageto showcase Projects & Certifications

• Live Individual & Group Sessionsto resolve queries, Discuss Progress and Study Plans.

• Personalized & Hands-OnSupport over Mail, Telephone for Query Resolution & Overall Learner Progress.

• Job-Oriented Industry Relevant Curriculumavailable at your fingertips curated by Global Industry Experts along with Live Sessions.

#### Instructors profiles

1 industry expert

Our instructors are industry experts along with a passion to teach.

12 years in the experience range

Instructors with 12 years extensive industry experience.

Areas of expertise

• Mathematics and Computing

#### Talk to our Team Directly

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