Explore the fundamentals of linear algebra, including its characteristics and its role in machine learning. Examine important concepts associated with linear algebra like the class of spaces, types of vector space, vector norms, linear product vector and theorems, and the various operations that can be performed on matrix. How to implement vector arithmetic, vector scalar multiplication, and matrix arithmetic using Python is also covered.

Linear Algebra and Probability: Fundamentals of Linear Algebra

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