# Linear Algebra and Probability: Fundamentals of Linear Algebra

Machine Learning    |    Intermediate
• 13 videos | 1h 40m 4s
• Includes Assessment
Likes 58
Explore the fundamentals of linear algebra, including characteristics and its role in machine learning, in this 13-video course. Learners can examine important concepts associated with linear algebra, such as the class of spaces, types of vector space, vector norms, linear product vector and theorems, and various operations that can be performed on matrix. Key concepts examined in this course include important classes of spaces associated with linear algebra; features of vector spaces and the different types of vector spaces and their application in distribution and Fourier analysis; and inner product spaces and the various theorems that are applied on inner product spaces. Next, you will learn how to implement vector arithmetic by using Python; learn how to implement vector scalar multiplication with Python; and learn the concept and different types of vector norms. Finally, learn how to implement matrix-matrix multiplication, matrix-vector multiplication, and matric-scalar multiplication by using Python; and learn about matrix decomposition and the roles of Eigenvectors and Eigenvalues in machine learning.

## WHAT YOU WILL LEARN

• discover the key concepts covered in this course identify the essential characteristics of linear algebra and its role in machine learning implementations list the important classes of spaces associated with linear algebra describe features of vector spaces and list the different types of vector spaces and their application in distribution and Fourier analysis describe the concept of inner product spaces and the various theorems that are applied on inner product spaces demonstrate how to implement vector arithmetic using Python demonstrate how to implement vector scalar multiplication using Python
• describe the concept and different types of vector norms implement matrix-matrix multiplication, matrix-vector multiplication, and matric-scalar multiplication using Python recognize operations that can be performed on matrix, such as matrix norms and matrix identities recognize how the trace, determinant, inverse, and transpose operations are applied on matrix describe matrix decomposition, using eigendecomposition, and the role of Eigenvectors and Eigenvalues describe the features of vector spaces, recall the different types of vector norms, and implement matrix-matrix multiplication, matrix-vector multiplication, and matric-scalar multiplication using Python

## IN THIS COURSE

• In this video, find out how to identify the essential characteristics of linear algebra and its role in machine learning implementations.
• 3.  Class of Spaces
Upon completion of this video, you will be able to list the important classes of spaces associated with linear algebra.
• 4.  Types of Vector Space
Upon completion of this video, you will be able to describe features of vector spaces and list the different types of vector spaces and their applications in distribution and Fourier analysis.
• 5.  Linear Product Vector and Theorems
After completing this video, you will be able to describe the concept of inner product spaces and the various theorems that apply to inner product spaces.
• 6.  Vector Arithmetic
In this video, you will learn how to implement vector arithmetic using Python.
• 7.  Vector Scalar Multiplication
In this video, you will learn how to implement vector scalar multiplication using Python.
• 8.  Vector Norms
Upon completion of this video, you will be able to describe the concept of vector norms and different types of vector norms.
• 9.  Matrix Arithmetic
In this video, learn how to implement matrix-matrix multiplication, matrix-vector multiplication, and matrix-scalar multiplication using Python.
• 10.  Working with Matrix
Upon completion of this video, you will be able to recognize operations that can be performed on a matrix, such as matrix norms and matrix identities.
• 11.  Matrix Operations
Upon completion of this video, you will be able to recognize how to apply the trace, determinant, inverse, and transpose operations on a matrix.
• 12.  Matrix Decomposition
Upon completion of this video, you will be able to describe matrix decomposition using eigendecomposition, and the role of eigenvectors and eigenvalues.
• 13.  Exercise: Vector Norms and Matrix Arithmetic
After completing this video, you will be able to describe the features of vector spaces, recall the different types of vector norms, and implement matrix-matrix multiplication, matrix-vector multiplication, and matrix-scalar multiplication using Python.

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