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Linear Algebra

  1. Vectors
    1. Scalars
    2. Vectors vs Sets
    3. Addition and Subtraction
    4. Scalar Multiplication
    5. Zero Vectors
    6. Linear Combinations
    7. Real Dot Product
    8. Length of a Vector
    9. Orthogonal Vectors
    10. Parallel Vectors
    11. Angle Between Vectors
    12. Unit Vectors
  2. Matrices
    1. Notation
    2. Indexing
    3. Submatrices
    4. Matrix-by-Vector Product
    5. Addition and Subtraction
    6. Scalar Multiplication
    7. Transpose
    8. Symmetries
    9. Matrix Multiplication
    10. Identity Matrix
    11. Non-Negative Integer Powers
    12. Reverse Order Law of Transposition
  3. Linear Systems
    1. Inverse Matrices
    2. Singular Matrices
    3. Linear Dependence
    4. Solutions
  4. Planes
    1. Vector Cross Product
  5. Gaussian Elimination
Linear Algebra ›Vectors ›Scalars

Scalars

This short lesson is mainly about terminology. It is important that the concept of a scalar is clear, as everything else builds on top of this concept and I will be referring to it later in the course.

A scalar gets its name from the verb “to scale”. That is because it contains the notion of “how much bigger or smaller do we want something”. It “scales” something.

Usually, in most basic mathematics, this will be some element of R\mathbb{R}R (the real numbers). Some examples include numbers like 111, 444, π\piπ, 2\sqrt{2}2​.

We will get back to the concept of “scaling” when we talk about scalar multiplication.

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Vectors - Introduction
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Differences Between Vectors and Sets
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