Lecture 23. Kernel and Image

0:00 Definitions of the Kernel and the Image of a linear transformation 1:44 Example: Kernel and Image of a projection 5:13 Example: Kernel and Image of differentiation R[X] → R[X] 7:44 Example: Kernel and Image of differentiation of quadratic polynomials 10:58 Example: Kernel and Image of a rotation 13:10 Kernel and Image are subspaces 24:50 Kernel of a matrix is its Nullspace, Image is the Column space 30:42 Formula: dim Ker(T) + dim Im(T) = dim V 32:58 Example: Finding bases of the kernel and the image of a matrix 45:01 Injective and surjective functions 49:27 Digression into logic: Negations of statements with quantifiers 1:07:08 Injective and surjective linear transformations In this lecture, we introduce the notions of kernel and image of a linear transformation. We also discuss injectivity and surjectivity of linear transformations. This is a Lecture in the "Linear Algebra" course for students specializing in mathematics.