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In this course, you will learn :
- Vectors can be added and scaled geometrically or component-wise.
- Give an example of a linear combination of two vectors.
- A vector can be written as a linear combination of other vectors.
- In simple cases, determine whether a vector is in the span of others.
- Write the geometric definition of the dot product involving lengths and angles, as well as the definition of the dot product of two vectors written in components.
- Calculate the dot products and lengths.
- Determine the angle formed by two vectors.
- Define and generate unit vectors.
- Demonstrate understanding of and application of Cauchy-Schwarz and Triangle Inequality.
Syllabus :
1. Vectors
- Geometric Vectors
- Remarks on Geometric Vectors
- Example: Application of Geometric Vectors
- Algebraic Vectors
- Examples: Algebraic Vectors
- Linear Combination
- Span of a Set of Vectors
- The Norm
- Theorems Related to the Norm
- The Dot Product
- Remarks and Examples of Dot Product
- Theorems Related to the Dot Product
- Cauchy-Schwarz Inequality and Triangle Inequality
