Linear Algebra: Introduction to Vectors

Course Overview

What does this course tell?
(Please note that the following overview content is from the original platform)


Introduction to Vectors.
Length of a Vector in 2 Dimensions (examples).
1.1 Vector Addition.
1.1 Multiplying a Vector by a Scalar.
1.1 Vector Subtraction.
1.1 Vectors with 3 components (3 dimensions).
1.1 Length of a 3-Dimensional Vector.
1.1 Definition of R^n.
1.1 Length of a Vector.
1.2 Proof: Vector Addition is Commutative and Associative.
1.2 Algebraic Properties of Vectors.
1.3 Definition of the Dot Product.
1.3 Dot Product - Angle Between Two Vectors.
1.3 Find the Angle Between Two Vectors (example).
1.3 Orthogonal Vectors.
1.3 Proof about the Diagonals of a Parellelogram.


We consider the value of this course from multiple aspects, and finally summarize it for you from three aspects: personal skills, career development, and further study:
(Kindly be aware that our content is optimized by AI tools while also undergoing moderation carefully from our editorial staff.)
What skills and knowledge will you acquire during this course?
By taking this course, learners will acquire skills and knowledge in linear algebra and vector operations, including vector addition, subtraction, multiplication, and division, as well as the algebraic properties of vectors. They will also learn how to calculate the length of a vector, the dot product, and the angle between two vectors. Additionally, learners will gain an understanding of the proof about the diagonals of a parallelogram. These skills and knowledge can be applied to a variety of real-world problems, such as calculating the displacement of an object in two or three dimensions, calculating the angle between two vectors, or determining if two vectors are orthogonal. Furthermore, these skills and knowledge can be used in various career paths, such as data science, machine learning engineering, robotics engineering, and financial analysis.

How does this course contribute to professional growth?
This course provides learners with a comprehensive overview of the fundamentals of vectors. By gaining a comprehensive understanding of the topics, learners will be able to develop a strong foundation in linear algebra and vector operations. This knowledge can be applied to a variety of real-world problems, such as calculating the displacement of an object in two or three dimensions, calculating the angle between two vectors, or solving equations and proving theorems. Furthermore, this course can help learners pursue a career in data science, machine learning engineering, robotics engineering, or financial analysis, all of which are expected to continue to grow in the coming years. As such, this course can contribute to professional growth by providing learners with the necessary skills and knowledge to pursue these career paths.

Is this course suitable for preparing further education?
Yes, This course provides a comprehensive overview of the fundamentals of vectors, including vector addition, subtraction, multiplication, and division, as well as the algebraic properties of vectors. Learners will gain an understanding of the length of a vector in two dimensions, the dot product, and the angle between two vectors. Additionally, they will learn how to apply the concepts to real-world problems and develop a strong foundation in linear algebra and vector operations. This knowledge can be applied to a variety of career paths, such as data science, machine learning engineering, robotics engineering, and financial analysis.