trustle > EngliSea > Corona Safe Schooling > mathematics > ￤math > 32 Linear Algebra |

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01 Vectors, what even are they?

The fundamental, root-of-it-all building block of linear algebra is the vector, so it's worth making sure that we're all on the same page about what exactly a vector is.

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The fundamental, root-of-it-all building block of linear algebra is the vector, so it's worth making sure that we're all on the same page about what exactly a vector is.

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02 Linear combinations, span and basis vectors

Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

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Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

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03 Linear transformations and matrices

Linear transformations and matrices | Essence of linear algebra, chapter 3

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Linear transformations and matrices | Essence of linear algebra, chapter 3

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04 Matrix multiplication as composition

Matrix multiplication as composition | Essence of linear algebra, chapter 4

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Matrix multiplication as composition | Essence of linear algebra, chapter 4

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07 How to organize, add and multiply matrices

By now, I'm sure that in just anything you do in your life, you need numbers. In particular, though some fields don't just need a few numbers, they need lots of them. How do you keep track of those numbers?

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By now, I'm sure that in just anything you do in your life, you need numbers. In particular, though some fields don't just need a few numbers, they need lots of them. How do you keep track of those numbers?

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12.3 Dot Product Part 1

Given two nonzero vectors in two or three dimensions, their dot product is the product of the magnitudes times cosine of the angle between the two vectors.

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Given two nonzero vectors in two or three dimensions, their dot product is the product of the magnitudes times cosine of the angle between the two vectors.

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12.4 Cross Product Part 1

Given two nonzero vectors in two or three dimensions, their cross product is a vector with magnitude equal to the product of the magnitudes of the vectors times the sine of the angle between the vectors and direction perpendicular to the vectors.

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Given two nonzero vectors in two or three dimensions, their cross product is a vector with magnitude equal to the product of the magnitudes of the vectors times the sine of the angle between the vectors and direction perpendicular to the vectors.

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**Dave**

• 01 Introduction to Vectors and Their Operations • 02 The Vector Dot Product • 03 Introduction to Linear Algebra • 04 Understanding Matrices and Matrix Notation • 05 Elementary Row Operations and Gauss-Jordan Elimination • 06 Types of Matrices and Matrix Addition • 07 Matrix Multiplication and Associated Properties • 08 Evaluating the Determinant of a Matrix • 09 The Vector Cross Product • 10 Inverse Matrices and Their Properties • Orthogonality and Orthonormality

• 01 Introduction to Vectors and Their Operations • 02 The Vector Dot Product • 03 Introduction to Linear Algebra • 04 Understanding Matrices and Matrix Notation • 05 Elementary Row Operations and Gauss-Jordan Elimination • 06 Types of Matrices and Matrix Addition • 07 Matrix Multiplication and Associated Properties • 08 Evaluating the Determinant of a Matrix • 09 The Vector Cross Product • 10 Inverse Matrices and Their Properties • Orthogonality and Orthonormality

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**Matthew Salomone**

• Matthew Salomone • 202W.00 Getting Started • 202W.01.1 What is Linear Algebra? • 202W.02 The parametric solution set of a linear system • 202W.02A Numbers of variables and equations means... • 202W.02B What do pivots mean? 2x2 examples • 202W.02C What do pivots mean? 3x3 examples • 202W.03C Linear systems and linear combinations • 202W.03D Intro to Matrices and Matrix Multiplication • 202W.03E What does linear algebra "look like?" • 202W.04E Linear Independence Activity 2.4.3

• Matthew Salomone • 202W.00 Getting Started • 202W.01.1 What is Linear Algebra? • 202W.02 The parametric solution set of a linear system • 202W.02A Numbers of variables and equations means... • 202W.02B What do pivots mean? 2x2 examples • 202W.02C What do pivots mean? 3x3 examples • 202W.03C Linear systems and linear combinations • 202W.03D Intro to Matrices and Matrix Multiplication • 202W.03E What does linear algebra "look like?" • 202W.04E Linear Independence Activity 2.4.3

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**Tensor**

• 01 Motivation • 02 Tensor Definition • 03 Correction on Forward + Backward Transforms • 03 Forward and Backward Transformations (contains error; read description! • 04 Vector definition • 05 Vector Transformation Rules • 06 What are Covectors?

• 01 Motivation • 02 Tensor Definition • 03 Correction on Forward + Backward Transforms • 03 Forward and Backward Transformations (contains error; read description! • 04 Vector definition • 05 Vector Transformation Rules • 06 What are Covectors?