🛍 Check out my math fashion brand! ❤️ Support the production of this course by joining Wrath of Math to access all my Linear Algebra videos plus lecture notes at the premium tier! Linear Algebra course: Linear Algebra exercises: Get the textbook for this course! Business Inquiries: wrathofmathlessons@ We introduce one to one and onto linear transformations. These are properties you may be familiar with, one to one is also called "injective" and onto is called "surjective". These properties are important, and as we'll see in later lectures, many nice things can be said about linear transformations with either or both of these properties. We'll show several examples of linear transformations that are onto or one-to-one or neither. We'll prove a theorem establishing an equivalence between a linear transformation being one-to-one, being onto, and having the zero space as its kernel (provided the domain and codomain have the same finite dimension). #linearalgebra ★DONATE★ ◆ Support Wrath of Math on Patreon: ◆ Donate on PayPal: Follow Wrath of Math on... ● Instagram: ● TikTok: @wrathofmathedu ● X: 0:00 Intro 0:32 Definition of One-to-One and Onto 1:19 Visualize the Definitions 3:14 Zero Kernel is same as One-to-One 6:03 Rotation is One to One and Onto 6:46 Projection onto xy Plane is Neither One to One nor Onto 7:55 Transpose is One to One and Onto 9:13 Zero Transformation is Neither One to One nor Onto 10:01 One to One but not Onto 11:31 An Onto Equivalence 15:14 Conclusion