One-to-One and Onto Linear Transformations in Linear Algebra

Explore one-to-one and onto linear transformations in this 16-minute video lecture from the Wrath of Math Linear Algebra course. Delve into the properties of injective and surjective transformations, understanding their importance in linear algebra. Examine various examples of linear transformations, including rotations, projections, and transpositions, to illustrate these concepts. Learn about the equivalence between one-to-one transformations, onto transformations, and those with zero kernels in finite-dimensional spaces. Gain insights into the theoretical foundations and practical applications of these transformations through clear explanations and visual representations.

Intro
Definition of One-to-One and Onto
Visualize the Definitions
Zero Kernel is same as One-to-One
Rotation is One to One and Onto
Projection onto xy Plane is Neither One to One nor Onto
Transpose is One to One and Onto
Zero Transformation is Neither One to One nor Onto
One to One but not Onto
An Onto Equivalence
Conclusion