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Rank and Nullity of Linear Transformations | Linear Algebra
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We introduce the concepts of rank and nullity of general linear transformations, these are natural extension of rank and nullity for matrices. If T is a linear transformation with a finite-dimension kernel, then the dimension of the kernel is the nullity. If T has a finite-dimensional range, then the dimension of the range is the rank. We'll also see the Dimension Theorem for linear transformations, stating rank+nullity=dimension of domain space. We'll see several examples of finding the rank and nullity of linear transformations. #linearalgebra
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0:00 Intro
0:17 Definition of Rank and Nullity
1:17 Dimension Theorem for Linear Transformations
2:58 Dilation Transformation Rank and Nullity
4:39 Using Dimension Theorem to find Rank
8:18 Conclusion
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Join Wrath of Math to get exclusive videos, lecture notes, and more:
0:00 Intro
0:17 Definition of Rank and Nullity
1:17 Dimension Theorem for Linear Transformations
2:58 Dilation Transformation Rank and Nullity
4:39 Using Dimension Theorem to find Rank
8:18 Conclusion
★DONATE★
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
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