This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]
This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.
This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This 20-minute video lesson looks at the relationship between left nullspace, rowspace, column space and nullspace. [Linear Algebra playlist: Lesson 98 of 143]
This 14-minute video lesson provides an Introduction to linear transformations.
Showing that matrix products are associative. Created by Sal Khan.
This lesson discusses how to identify sets of numbers as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
This site teaches Quantities to High Schoolers through a series of 116 questions and interactive activities aligned to 4 Common Core mathematics skills.
This site teaches The Complex Number System to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.
This site teaches The Real Number System to High Schoolers through a series of 1090 questions and interactive activities aligned to 8 Common Core mathematics skills.
This site teaches Vector and Matrix Quantities to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.
This 15-minute video lesson gives an example involving the preimage of a set under a transformation. It also gives a definition of kernel of a transformation.
The addition rule for probability is explained using Venn Diagrams. [Probability playlist: Lesson 3 of 29]
This lesson introduces basic probability. [Probability playlist: Lesson 1 of 29]
This lesson is a birthday problem that determines the probability that at least 2 people in a room of 30 share the same birthday. [Probability playlist: Lesson 17 of 29]
This lesson presents an example of dependent probability. [Probability playlist: Lesson 10 of 29]