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Power Method for Dominant Eigenvalues and Eigenvectors | Linear Algebra
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Continuing our chapter on numerical analysis, we introduce the power method with maximum entry scaling and with Euclidean scaling for approximating dominant eigenvectors and dominant eigenvalues of symmetric matrices. We'll define power sequences and dominant eigenvalues and dominant eigenvectors. We'll do an example performing six iterations of the power method for approximating dominant eigenvectors and then use the Rayleigh quotient to approximate the corresponding dominant eigenvalue. #linearalgebra
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Power Method Proof: (coming soon)
Decomposing Ax into Eigenspace Projections: (coming soon)
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0:00 Intro
0:18 Definition of Power Sequence and Dominant Eigenvalues/Eigenvectors
1:09 Dominant Eigenvalue Example
1:59 Power Method Approximation
3:31 If the Dominant Eigenvalue is Negative
4:35 Rayleigh Quotient
5:47 Using the Power Method
7:52 Start
9:08 Arriving at Approximation
10:55 Issue of Scale
12:00 Maximum Entry Scaling
14:00 Euclidean Scaling
15:35 Geometric Intuition
19:47 Conclusion
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
Join Wrath of Math to get exclusive videos, lecture notes, and more:
Power Method Proof: (coming soon)
Decomposing Ax into Eigenspace Projections: (coming soon)
★DONATE★
0:00 Intro
0:18 Definition of Power Sequence and Dominant Eigenvalues/Eigenvectors
1:09 Dominant Eigenvalue Example
1:59 Power Method Approximation
3:31 If the Dominant Eigenvalue is Negative
4:35 Rayleigh Quotient
5:47 Using the Power Method
7:52 Start
9:08 Arriving at Approximation
10:55 Issue of Scale
12:00 Maximum Entry Scaling
14:00 Euclidean Scaling
15:35 Geometric Intuition
19:47 Conclusion
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
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