Civil Engineering (CE) Exam > Civil Engineering (CE) Videos > Engineering Mathematics > Linear Transformation & Examples of Linear Transformation - Linear Algebra
Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
|
65 videos|120 docs|94 tests
|
FAQs on Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture - Engineering Mathematics - Civil Engineering (CE)
| 1. What is a linear transformation? |  |
A linear transformation, also known as a linear map, is a function between two vector spaces that preserves the operations of addition and scalar multiplication. It maps vectors from one space to another in a linear manner, meaning that it maintains the linearity property: T(a*u + b*v) = a*T(u) + b*T(v), where T represents the linear transformation, u and v are vectors, and a and b are scalars.
| 2. What are some examples of linear transformations? | |
Some examples of linear transformations include:
- Scaling: The transformation that stretches or shrinks a vector by a constant factor in each dimension.
- Rotation: The transformation that rotates a vector around a fixed point or axis.
- Reflection: The transformation that mirrors a vector across a line or plane.
- Projection: The transformation that projects a vector onto a lower-dimensional subspace.
- Translation: The transformation that shifts a vector by a fixed amount in each dimension.
| 3. How can I determine if a transformation is linear? | |
To determine if a transformation is linear, you need to check if it preserves the linearity property. This means that the transformation should satisfy the following two conditions:
1. T(u + v) = T(u) + T(v) for any vectors u and v.
2. T(c*u) = c*T(u) for any scalar c and vector u.
If both of these conditions hold true for a given transformation, then it is linear. However, if either condition fails for any pair of vectors or scalars, the transformation is not linear.
| 4. Can a linear transformation change the dimension of a vector space? | |
No, a linear transformation cannot change the dimension of a vector space. The dimension of the vector space is determined by the number of linearly independent vectors needed to span the space. Since a linear transformation preserves the operations of addition and scalar multiplication, it cannot introduce new linearly independent vectors or remove existing ones. Therefore, the dimension of the vector space remains the same after a linear transformation.
| 5. How are linear transformations represented mathematically? | |
Linear transformations can be represented mathematically using matrices. For example, consider a linear transformation T that maps vectors from a vector space V to another vector space W. If {v1, v2, ..., vn} is a basis for V and {w1, w2, ..., wm} is a basis for W, then T can be represented by an m x n matrix A. Each column of the matrix corresponds to the image of the corresponding basis vector in V under the transformation T. The result of applying the transformation to a vector v can be obtained by multiplying the matrix A with the column vector representation of v.
Related Exams
About this Video
|
4.69/5 Rating |
|
Dec 24, 2024 Last updated |
Video Description: Linear Transformation & Examples of Linear Transformation - Linear Algebra for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation.
The notes and questions for Linear Transformation & Examples of Linear Transformation - Linear Algebra have been prepared according to the Civil Engineering (CE) exam syllabus.
Information about Linear Transformation & Examples of Linear Transformation - Linear Algebra covers all important topics for Civil Engineering (CE) 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Linear Transformation & Examples of Linear Transformation - Linear Algebra.
Introduction of Linear Transformation & Examples of Linear Transformation - Linear Algebra in English is available as part of our Engineering Mathematics for Civil Engineering (CE) & Linear Transformation & Examples of Linear Transformation - Linear Algebra in
Hindi for Engineering Mathematics course. Download more important topics related with notes, lectures and mock test series for
Civil Engineering (CE) Exam by signing up for free.
Description
Video Lecture & Questions for Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE) - Civil Engineering (CE) full syllabus preparation | Free video for Civil Engineering (CE) exam to prepare for Engineering Mathematics.
Information about Linear Transformation & Examples of Linear Transformation - Linear Algebra
Here you can find the meaning of Linear Transformation & Examples of Linear Transformation - Linear Algebra defined & explained in the simplest way possible.
Besides explaining types of Linear Transformation & Examples of Linear Transformation - Linear Algebra theory, EduRev gives you an ample number of questions to practice Linear Transformation & Examples of Linear Transformation - Linear Algebra tests,
examples and also practice Civil Engineering (CE) tests.
|
65 videos|120 docs|94 tests
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Objective type Questions
,past year papers
,ppt
,MCQs
,Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,shortcuts and tricks
,mock tests for examination
,Sample Paper
,study material
,Viva Questions
,Important questions
,video lectures
,practice quizzes
,Semester Notes
,Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,Previous Year Questions with Solutions
,Exam
,Extra Questions
,Linear Transformation & Examples of Linear Transformation - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,Free
,Summary
;
Study Linear Transformation & Examples of Linear Transformation - Linear Algebra on the App
Students of Civil Engineering (CE) can study Linear Transformation & Examples of Linear Transformation - Linear Algebra alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Linear Transformation & Examples of Linear Transformation - Linear Algebra,
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 Transformation & Examples of Linear Transformation - Linear Algebra is prepared as per the latest Civil Engineering (CE) syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup