Kernel and Range of Linear Transformations | Linear Algebra
We introduce the kernel and range of a linear transformation. The kernel is the extension of the null space to general linear transformations and the range is the extension of the column space to general linear transformations. We go over the definitions of these terms, see several examples, and then prove a theorem stating the kernel is a subspace of the domain and the range is a subspace of the codomain. #linearalgebra
Join Wrath of Math to get exclusive videos, lecture notes, and more:
/ @wrathofmath
Linear Transformations in Vector Spaces: • General Linear Transformations on Vec...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
Get the textbook for this course! https://amzn.to/43xAWEz
0:00 Intro
1:54 Definitions of Kernel and Range
4:06 Zero Transformation Kernel and Range
4:59 Kernel and Range of Projection onto xy Plane
6:51 Kernel and Range of Rotation
7:38 Subspace Theorem
8:14 Kernel is a Subspace
10:28 Range is a Subspace
13:20 Conclusion
★DONATE★
◆ Support Wrath of Math on Patreon: / wrathofmathlessons
◆ Donate on PayPal: https://www.paypal.me/wrathofmath
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● TikTok: / wrathofmathedu
● X: https://x.com/wrathofmathedu
● Facebook: / wrathofmath
Смотрите видео Kernel and Range of Linear Transformations | Linear Algebra онлайн без регистрации, длительностью часов минут секунд в хорошем качестве. Это видео добавил пользователь Wrath of Math 21 Август 2024, не забудьте поделиться им ссылкой с друзьями и знакомыми, на нашем сайте его посмотрели 3,817 раз и оно понравилось 105 людям.