Become a Linear Algebra Master

Course Name : Become a Linear Algebra Master
Students : 41,940
Duration : 15 hrs & 172 downloadable resources
Avg Rating : 4.8 (5,791 ratings)
Original Price : $119.99
Discount Price : $13
Instructor / Provider : Krista King, Udemy
Course Type : Self Paced Online Course. Lifetime Access
Coupon : Click on ENROLL NOW to apply discount code

What You’ll Learn:

Master Linear Algebra Concepts

• Perform operations on single and multiple matrices, including solving linear systems, Gauss-Jordan elimination, and matrix multiplication.
• Understand matrix-vector relationships, including linear combinations, span, and subspaces.
• Explore dot products and cross products, including inequalities like Cauchy-Schwarz and the vector triangle inequality.
• Analyze matrix-vector products, focusing on null spaces, column spaces, and solving systems of equations.
• Learn about transformations, including projections, linear transformations, and their compositions.

Advanced Topics in Linear Algebra

• Dive into invertible matrices, singular matrices, and solving systems using matrix inverses.
• Explore determinants, their properties, and applications such as Cramer’s Rule.
• Work with transposes, null spaces, column spaces, and determinant properties of transposed matrices.
• Study orthogonality, orthogonal complements, projections onto subspaces, and least squares solutions.
• Master orthonormal bases and the Gram-Schmidt process for basis conversion.
• Understand eigenvalues and eigenvectors, their eigenspaces, and applications in three-dimensional spaces.

Frequently Bought Together

Course Modules:

Matrix Operations

1. Operations on single matrices:
   • Solving linear systems
   • Gauss-Jordan elimination
2. Operations on two matrices:
   • Matrix multiplication
   • Elimination matrices

Vectors and Subspaces

• Matrices as vectors:
  • Linear combinations, span, and subspaces
  • Linear independence
• Matrix-vector products:
  • Null spaces and column spaces
  • Solving Ax = b

Vector Products and Transformations

• Dot products and cross products:
  • Cauchy-Schwarz inequality
  • Vector triangle inequality
• Transformations:
  • Linear transformations and projections
  • Composition of transformations

Inverses and Determinants

• Inverses:
  • Invertible vs. singular matrices
  • Solving systems with matrix inverses
• Determinants:
  • Properties of triangular matrices
  • Cramer’s Rule

Transposes and Spaces

• Transposes:
  • Determinants of transposed matrices
  • Null (left null) spaces and column (row) spaces of transposes

Orthogonality and Basis Changes

• Orthogonality:
  • Orthogonal complements and projections
  • Least squares solutions and basis transformations
• Orthonormal bases and Gram-Schmidt:
  • Defining orthonormal bases
  • Converting to orthonormal bases using the Gram-Schmidt process

Eigenvalues and Eigenvectors

• Finding eigenvalues and eigenvectors:
  • Associated eigenspaces
  • Applications in three-dimensional transformations

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