linear algebra

Linear Algebra Essentials

Introduction to Linear Algebra

linear algebra

Pre-Requisites

Mastering of Linear Algebra

Basic Definitions and Notation, Vectors and Vector Operations, Introduction to Matrices

Systems of Linear Equations

Solving Systems Using Row Reduction, Consistency and Inconsistency of Systems, Applications of Linear Systems 

Matrices and Determinants

Matrix Operations and Properties, Calculating Determinants, Inverse Matrices and Cramer's Rule  

Vector Spaces and Subspaces

Definitions of Vector Spaces, Linear Independence and Span, Basis and Dimension 

Matrices & Vector Plain

Eigenvalues and Eigenvectors

Finding the Characteristic Equation, Diagonalization of Matrices, Applications of Eigenvalues and Eigenvectors

Orthogonality

Orthogonality and Least Squares

Dot Product and Orthogonal Vectors, Orthogonal Projections and the Gram-Schmidt Process, Least Squares Solutions

Linear Transformations and Applications

Definition and Examples of Linear Transformations, Kernel, Image, and Matrix Representations, Change of Basis and Coordinate Systems 

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Personalized, interactive learning experiences delivered through a virtual/online platform, tailored to each student’s unique needs and schedule.  
(Ages: 8yrs - College/Adult)

Self-paced Pre-recorded Sessions

Pre-recorded class/sessions using a step-by-step approach to build confidence and problem-solving skills. 
(Ages: 14yrs - 18yrs)

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Frequently Asked Questions

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Students should currently be enrolled in a math program/class or have taken the class in the past.

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Answers to Common Questions

Extended Topics

Advanced Topics and Wrap-Up

Inner Product Spaces and Norms, Jordan Canonical Form and Advanced Diagonalization, Review and Final Concepts