수학으로부터 인류를 자유롭게 하라(선형대수학 Part.I) - 벡터기하학

Lecture.1-1-5 Zero / Unit Vectors

Lecture.1-1-6 Equal / Opposite Vectors

Lecture.1-2-1 Vector Addition - Parallelogram Method

Lecture.1-2-2 Vector Addition - Tip-to-Tail Method

Lecture.1-2-3 Algebraic Properties of Vector Addition

Lecture.1-2-4 Review; The Cosine Rule and Angles

Lecture.1-2-5 The Magnitude of Vector Addition

Lecture.1-3-1 Positive Scalar Multiplication

Lecture.1-3-2 Negative Scalar Multiplication

Lecture.1-3-3 Scalar Multiplication

Lecture.1-3-4 Algebraic Properties of Scalar Multiplication

Lecture.1-3-5 Parallel Vectors

Lecture.1-4-1 Vector Subtraction

Lecture.1-4-2 Vector Subtraction - Examples

Lecture.1-4-3 Algebraic Properties of Vector Subtraction

Lecture.1-5 Vector Decomposition

Lecture.2-1-5 Vectors on the Coord. Space

Lecture.2-2-1 From Chaos to Order

Lecture.2-2-2 Position Vectors

Lecture.2-2-3 Vector Spaces

Lecture.2-2-4 New Vector Notations

Lecture.2-2-5 Equal / Opposite Vectors

Lecture.2-3-1 Norms of 2D Vectors

Lecture.2-3-2 Norms of 3D Vectors

Lecture.2-3-3 Zero / Unit Vectors

Lecture.2-4 Circles and Spheres

Lecture.3-1-1 Direction Angles

Lecture.3-1-2 Direction Angles and Intervals

Lecture.3-1-3 Direction Angles and Quadrants

Lecture.3-1-4 Reflections and Direction Angles

Lecture.3-1-5 Reflections and Direction Angles - Examples

Lecture.3-1-6 Review; Trigonometric Functions

Lecture.3-1-7 Direction Cosines(1/2)

Lecture.3-1-8 Direction Cosines(2/2)

Lecture.3-1-9 Reflections and Direction Cosines

Lecture.3-2-1 From Direction Angles to Coordinates

Lecture.3-2-2 From Coordinates to Direction Angles

Lecture.3-2-3 Reflections of 2D Vectors

Lecture.3-3-1 Direction Angles and Cosines of 3D Vectors

Lecture.3-3-2 Directions and Coordinates of 3D Vectors

Lecture.3-3-3 Reflections over Planes(3D)

Lecture.3-3-4 Reflections over Axes(3D)

Lecture.3-4 The Sum of Squared Direction Cosines

Lecture.3-5 Rotating Vectors

Lecture.4-0 Introduction to the Chapter4

Lecture.4-1-1 Vector Addition

Lecture.4-1-2 Commutativity of Vector Addition

Lecture.4-1-3 Associativity of Vector Addition

Lecture.4-1-4 Additive Identity and Inverse

Lecture.4-2-1 Scalar Multiplication

Lecture.4-2-2 The Associativity of Scalar Multiplication

Lecture.4-2-3 The Distributivity of Scalar Multiplication

Lecture.4-2-4 Scalar Multiplication and Norms and Directions

Lecture.4-3-1 Vector Subtraction

Lecture.4-3-2 Algebraic Properties of Vector Subtraction

Lecture.4-3-3 The Distance between Vectors

Lecture.4-4-1 Vector Equations - Case1

Lecture.4-4-2 Vector Equations - Case2, 3

Lecture.4-4-3 Vector Equations - Case4

Lecture.4-5 Normalizing Vectors

Lecture.4-6-1 Vector Decomposition

Lecture.4-6-2 Decomposition with Standard Unit Vectors

Lecture.5-0 Introduction to the Chapter5

Lecture.5-1-1 The Algebraic Definition of Dot Product

Lecture.5-1-2 Commutativity of Dot Product

Lecture.5-1-3 Antiassociativity of Dot Product

Lecture.5-1-4 Distributivity of Dot Product

Lecture.5-1-5 Homogeneity of Dot Product

Lecture.5-1-6 Other Properties of Dot Product

Lecture.5-1-7 Simplifying Vector Calculations

Lecture.5-1-8 Dot Product and Linearity

Lecture.5-2-1 Dot Product with Ones and Zeros

Lecture.5-2-2 Self Dot Products and Norms

Lecture.5-2-3 Vector Square Multiplication Formula

Lecture.5-3-1 The Geometric Definition of Dot Product

Lecture.5-3-2 Geometric Dot Product and Ares

Lecture.5-3-3 The Algebraic / Geometric Definitions

Lecture.5-3-4 Algebraic Properties of Dot Product

Lecture.5-3-5 Dot Products with Unit Vectors

Lecture.5-4-1 Dot Product wrt Angles

Lecture.5-4-2 Dot Product and Orthogonality

Lecture.5-4-3 Dot Product and Orthonormality

Lecture.5-4-4 Cosine Similarity

Lecture.5-5 Vector Equalities and Inequalities

Lecture.6-0 Introduction to Projections

Lecture.6-1-1 Scalar Projection

Lecture.6-1-2 Angles and the Signs of Scalar Projections

Lecture.6-1-3 Scalar Projections with Fixed Norms

Lecture.6-1-4 Scalar Projections with Fixed Angles

Lecture.6-1-5 Scalar Projections and Dot Products

Lecture.6-1-6 Scalar Projection onto Unit Vectors

Lecture.6-1-7 Anti-commutativity of Scalar Projection

Lecture.6-1-8 Distributivities of Scalar Projection

Lecture.6-1-9 Parallelity / Orthogonality and Scalar Projection

Lecture.6-2-1 Vector Projections

Lecture.6-2-2 Calculating Vector Projections

Lecture.6-2-3 Norms and Directions of Vector Projections

Lecture.6-2-4 Vector Projections onto Unit Vectors

Lecture.6-2-5 Anti-commutativity of Vector Projeciton

Lecture.6-2-6 Anti-associativity of Vector Projeciton

Lecture.6-2-7 Distributivities of Vector Projection

Lecture.6-2-8 Other Properties of Vector Projection

Lecture.6-3-1 Orthogonal Decompositions - Definition.1

Lecture.6-3-2 Orthogonal Decompositions - Definition.2

Lecture.6-3-3 Reflections over Vectors

Lecture.6-3-4 Properties of Reflections

Lecture.6-4-1 Introduction to Gram-Schmidt Process

Lecture.6-4-2 Gram-Schmidt Process on 2D Vectors

Lecture.6-4-3 Gram-Schmidt Process on 3D Vectors

Lecture.7-1-1 Linear Combinations

Lecture.7-1-2 Sets of Linear Combinations

Lecture.7-2-1 Spans

Lecture.7-2-2 Spans of a Vector

Lecture.7-2-3 Spans of Two Vectors

Lecture.7-2-4 Spans of Three Vectors

Lecture7-3-1 Linear Independence

Lecture7-3-2 Linear Independence - Two Vector Cases

Lecture7-3-3 Linear Independence - Three Vector Cases

Lecture8-1-1 Lines

Lecture8-1-2 Lines in the Slope-intercept Form

Lecture8-1-3 Lines in the Slope-point Form

Lecture8-1-4 Lines in the Two-points Form

Lecture8-1-5 Lines in the Standard Form