Khan Academy
Khan Academy: Properties of Matrix Multiplication: Zero Matrix
Explains what the zero matrix is and how it is used in matrix multiplication. [4:41]
Khan Academy
Khan Academy: Properties of Matrix Multiplication: Intro to Identity Matrix
Just as any number remains the same when multiplied by 1, any matrix remains the same when multiplied by the identity matrix. [7:59]
Khan Academy
Khan Academy: Another Example of a Projection Matrix
Figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.
Sophia Learning
Sophia: Dot Products: Lesson 2
This lesson introduces the concept of a dot product and its relationship to matrix operations. It is 2 of 6 in the series titled "Dot Products."
Sophia Learning
Sophia: Equality in Matrices: Lesson 4
This lesson discusses when two matrices are considered equal. This is part of a series of lessons on early concepts related to matrices. It is 4 of 4 in the series titled "Equality in Matrices."
Sophia Learning
Sophia: Finding the Dot Product: Lesson 2
This lesson goes over the steps for finding the dot product of a matrix. It is 2 of 7 in the series titled "Finding the Dot Product."
Sophia Learning
Sophia: Finding the Dot Product: Lesson 3
This lesson goes over the steps for finding the dot product of a matrix. It is 3 of 7 in the series titled "Finding the Dot Product."
Sophia Learning
Sophia: Finding the Dot Product: Lesson 5
This lesson goes over the steps for finding the dot product of a matrix. It is 5 of 7 in the series titled "Finding the Dot Product."
Sophia Learning
Sophia: Finding the Dot Product: Lesson 6
This lesson goes over the steps for finding the dot product of a matrix. It is 6 of 7 in the series titled "Finding the Dot Product."
Sophia Learning
Sophia: Finding the Dot Product: Lesson 1
This lesson goes over the steps for finding the dot product of a matrix. It is 1 of 7 in the series titled "Finding the Dot Product."
Sophia Learning
Sophia: Matrices
This lesson will introduce matrices and how to determine their dimensions.
Sophia Learning
Sophia: Matrix Elements: Lesson 3
This lesson defines the numbers appearing within a matrix as its elements. This is part of a group of lessons about parts of a matrix. It is 3 of 4 in the series titled "Matrix Elements."
Sophia Learning
Sophia: Matrix Multiplication: Lesson 4
This lesson introduces matrix multiplication, distinguishes it from multiplying by a scalar, and provides examples of the operation. It is 4 of 2 in the series titled "Matrix Multiplication."
Sophia Learning
Sophia: Matrix Multiplication: Lesson 8
This lesson introduces matrix multiplication, distinguishes it from multiplying by a scalar, and provides examples of the operation. It is 8 of 2 in the series titled "matrix multiplication."
Sophia Learning
Sophia: Minors: Lesson 5
This lesson defines minors and their relationship to determinants. It is 5 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Minors: Lesson 6
This lesson defines minors and their relationship to determinants. It is 6 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Minors: Lesson 1
This lesson defines minors and their relationship to determinants. It is 1 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Multiplying Matrices by Scalar Values: Lesson 2
This lesson explains how to multiply a matrix by a scalar. It is 2 of 5 in the series titled "Multiplying Matrices by Scalar Values."
Sophia Learning
Sophia: Multiplying Matrices by Scalar Values: Lesson 4
This lesson explains how to multiply a matrix by a scalar. It is 4 of 5 in the series titled "Multiplying Matrices by Scalar Values."
Sophia Learning
Sophia: Multiplying Matrix Rows: Lesson 10
This lesson demonstrates the multiplication of rows in a matrix. This is part of a series of lessons showing various matrix operations. It is 10 of 10 in the series titled "Multiplying Matrix Rows."
Sophia Learning
Sophia: Multiplying Matrix Rows: Lesson 5
This lesson demonstrates the multiplication of rows in a matrix. This is part of a series of lessons showing various matrix operations. It is 5 of 10 in the series titled "Multiplying Matrix Rows."
Sophia Learning
Sophia: Multiplying Matrix Rows: Lesson 6
This lesson demonstrates the multiplication of rows in a matrix. This is part of a series of lessons showing various matrix operations. It is 6 of 10 in the series titled "Multiplying Matrix Rows."
Sophia Learning
Sophia: Multiplying Matrix Rows: Lesson 7
This lesson demonstrates the multiplication of rows in a matrix. This is part of a series of lessons showing various matrix operations. It is 7 of 10 in the series titled "Multiplying Matrix Rows."
Sophia Learning
Sophia: Multiplying Matrix Rows: Lesson 8
This lesson demonstrates the multiplication of rows in a matrix. This is part of a series of lessons showing various matrix operations. It is 8 of 10 in the series titled "Multiplying Matrix Rows."