Eigenvalues and Eigenvectors | Properties and Important Result | Matrices

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This video lecture of Eigenvalues and Eigenvectors | Properties and Important Result | Matrices | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. What is Eigenvalues and Eigenvectors ?
2.How to find Eigenvalues and Eigenvectors Of Matrices ?
3. Important Results and Properties Of Eigenvalues and Eigenvectors
4. Short Trick To Find Eigenvalues and Eigenvectors Of Matrices.
5. Proof of Theorem sum of eigenvalues equals trace and Product of eigenvalues is Determinante.
6. Concepts of Algebraic Multiplicity and Geometric Multiplicity.
7. This is part Of Linear Algebra
#Eigenvalues #Eigenvectors #Properties #Matrices #LinearAlgebra #VectorSpace #LinearTransformation #LinearlyIndependent #Linearlydependent #EngineeringMahemaics #BSCMaths #GATE #IITJAM #CSIRNET
This Concept is very important in Engineering & Basic Science Students. This video is very useful for B.Sc./B.Tech & M.Sc./M.Tech. students also preparing for NET, GATE and IIT-JAM Aspirants.
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Time Stamp
Eigen values and Eigen vectors
0:00 | An intro
0:18 | Topic introduction
1:12 | Eigen value: Definition
5:08 | Note- Eigen vector: Definition & Example
10:14 | Other Key points
12:17 | Algebraic multiplicity
13:44 | Geometric multiplicity
14:34 | Properties of eigen values & eigen vectors
17:53 | Theorem: Product of eigen value=determinant & Sum of eigen value=trace
22:06 | Question 1
23:25 | Conclusion of video
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It's a great help for students

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Bhoot hi jayada acha h or sb smja ata h .

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people who only want to solve questions on eigen vectors should watch videos of Dr. Gajendra purohit and students who really want to understand what eigen vector means should watch videos of 3blue 1brown . But it is sad that very few students are actually interested in learning concepts of mathematics

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Please improve it sir

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At 9:24 When R2->R2-R1 shouldn't it be x2-x1 in R2? if we are applying an operation it should be applied overall na?

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No no the operation which we are applying are only applied on the matrix beside X and on the right hand side, that are not applied on the variable (i.e. on matrix X)
this is the rule.

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🙏🙏

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It's 11:53 pm, Tomorrow is my mathematics exam and this is the first time learning this topic

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[@mrfalcon7943]

Sir How to solve this....
For a given matrix A of order 3, | A |=32 and two of its Eigen values are 8 and 2 find the sum of the Eigen Values.

[@Ritesh_Chauhan_]

product of eigen values = determinant of the matrix,
=> |A| = 8*2*x
32 = 16x
Therefore, x = 2
Hence, sum of eigen values is 12.

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