Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Linear transformations
Linear transformations Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Linear transformations Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a linear transformation? |  |
A linear transformation is a mathematical function that maps vectors from one vector space to another, while preserving the straightness of lines and the origin. It can be represented by a matrix multiplication, where each element of the vector is multiplied by a corresponding element in the matrix and then summed up to obtain the transformed vector.
| 2. What are the properties of a linear transformation? | |
There are three main properties of a linear transformation:
1) Preservation of addition: For any two vectors u and v in the vector space, the linear transformation T(u+v) is equal to T(u) + T(v).
2) Preservation of scalar multiplication: For any scalar c and vector v, the linear transformation T(cv) is equal to cT(v).
3) Preservation of the origin: The linear transformation T(0) is equal to 0, where 0 represents the zero vector in the vector space.
| 3. How can we represent a linear transformation using matrices? | |
A linear transformation can be represented using matrices by defining a matrix that corresponds to the transformation. The columns of the matrix are formed by applying the transformation to the basis vectors of the vector space. When we multiply this matrix with a vector, we obtain the transformed vector.
| 4. What is the relationship between linear transformations and eigenvalues/eigenvectors? | |
Eigenvalues and eigenvectors are closely related to linear transformations. An eigenvector of a linear transformation is a non-zero vector that only gets scaled by the transformation, without changing its direction. The corresponding eigenvalue is the scalar value by which the eigenvector is scaled. Eigenvectors/eigenvalues provide important information about the behavior of linear transformations, such as their stretch or compression along certain directions.
| 5. Can all transformations be represented as linear transformations? | |
No, not all transformations can be represented as linear transformations. Linear transformations have specific properties, such as preserving addition and scalar multiplication, which many other transformations do not satisfy. Non-linear transformations, for example, may involve curves, rotations, or any other alteration of the shape or structure of the vectors being transformed.
About this Video
4.72/5
Rating
Sep 09, 2025
Last updated
Related Exams
Video Description: Linear transformations for Mathematics 2025 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Linear transformations have been prepared according to the Mathematics exam syllabus.
Information about Linear transformations covers all important topics for Mathematics 2025 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Linear transformations.
Introduction of Linear transformations in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Linear transformations in
Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Linear transformations Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.
Information about Linear transformations
Here you can find the meaning of Linear transformations defined & explained in the simplest way possible.
Besides explaining types of Linear transformations theory, EduRev gives you an ample number of questions to practice Linear transformations tests,
examples and also practice Mathematics tests.
Related Searches
Objective type Questions
,video lectures
,study material
,GATE
,Extra Questions
,MCQs
,Important questions
,CSIR NET
,Sample Paper
,CSIR NET
,UGC NET
,Free
,Linear transformations Video Lecture | Mathematics for IIT JAM
,past year papers
,CSIR NET
,Linear transformations Video Lecture | Mathematics for IIT JAM
,shortcuts and tricks
,practice quizzes
,mock tests for examination
,Exam
,GATE
,Previous Year Questions with Solutions
,Semester Notes
,ppt
,Summary
,UGC NET
,Linear transformations Video Lecture | Mathematics for IIT JAM
,UGC NET
,GATE
,Viva Questions
;
Study Linear transformations on the App
Students of Mathematics can study Linear transformations alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Linear transformations,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Linear transformations is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily