Vectors and spaces | Linear Algebra | Khan Academy (English)

   Thursday, July 15, 2021   

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Vectors and spaces | Linear Algebra | Khan Academy
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Lecture 1: Defining the angle between vectors

Lecture 2: Proof: Relationship between cross product and sin of angle

Lecture 3: Matrix vector products

Lecture 4: Point distance to plane

Lecture 5: Adding vectors

Lecture 6: Span and linear independence example

Lecture 7: Unit vector notation

Lecture 8: More on linear independence

Lecture 9: Showing relation between basis cols and pivot cols

Lecture 10: Showing that the candidate basis does span C(A)

Lecture 11: Introduction to linear independence

Lecture 12: Visualizing a column space as a plane in R3

Lecture 13: Dimension of the column space or rank

Lecture 14: Matrices: Reduced row echelon form 3

Lecture 15: Matrices: Reduced row echelon form 1

Lecture 16: Vector triangle inequality

Lecture 17: Linear combinations and span

Lecture 18: Defining a plane in R3 with a point and normal vector

Lecture 19: Vector dot product and vector length

Lecture 20: Multiplying a vector by a scalar

Lecture 21: Proof: Any subspace basis has same number of elements

Lecture 22: Vector intro for linear algebra

Lecture 23: Normal vector from plane equation

Lecture 24: Parametric representations of lines

Lecture 25: Vector intro for linear algebra

Lecture 26: Normal vector from plane equation

Lecture 27: Parametric representations of lines

Lecture 28: Introduction to the null space of a matrix

Lecture 29: Real coordinate spaces

Lecture 30: Matrices: Reduced row echelon form 2

Lecture 31: Cross product introduction

Lecture 32: Linear subspaces

Lecture 33: Null space 2: Calculating the null space of a matrix

Lecture 34: Proof of the Cauchy-Schwarz inequality

Lecture 35: Vector examples

Lecture 36: Proving vector dot product properties

Lecture 37: Column space of a matrix

Lecture 38: Dot and cross product comparison/intuition

Lecture 39: Distance between planes

Lecture 40: Null space 3: Relation to linear independence

Lecture 41: Basis of a subspace