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Learn linear algebra with these filled-in guided notes, the completed versions of the free notes used in my full Linear Algebra course on YouTube. These notes follow the entire video series and include detailed written explanations, step-by-step solutions, and fully worked examples for every major topic in an introductory linear algebra course. For the best learning experience, use these notes together with the corresponding video lessons.
Topics include:
• Solving linear systems and matrix methods
• Row operations, echelon forms, and matrix inverses
• Linear transformations and standard matrices
• Vector spaces, subspaces, basis, dimension, and rank
• Determinants and properties of determinants
• Eigenvalues, eigenvectors, eigenspaces, and diagonalization
• Orthogonality, projections, and the Gram–Schmidt process
• Applications across engineering, mathematics, and data science
Designed to support students throughout an entire semester, these notes provide a complete, structured resource for study, review, homework support, or classroom teaching.
• Purchasers may download and print for personal study.
• Teachers may use with their own students (print or digital).
• Sharing, uploading, reselling, or redistributing is strictly prohibited.
• For multi-teacher or school-wide licensing, email contact@understandthemath.com
Learn linear algebra with these filled-in guided notes, the completed versions of the free notes used in my full Linear Algebra course on YouTube. These notes follow the entire video series and include detailed written explanations, step-by-step solutions, and fully worked examples for every major topic in an introductory linear algebra course. For the best learning experience, use these notes together with the corresponding video lessons.
Topics include:
• Solving linear systems and matrix methods
• Row operations, echelon forms, and matrix inverses
• Linear transformations and standard matrices
• Vector spaces, subspaces, basis, dimension, and rank
• Determinants and properties of determinants
• Eigenvalues, eigenvectors, eigenspaces, and diagonalization
• Orthogonality, projections, and the Gram–Schmidt process
• Applications across engineering, mathematics, and data science
Designed to support students throughout an entire semester, these notes provide a complete, structured resource for study, review, homework support, or classroom teaching.
• Purchasers may download and print for personal study.
• Teachers may use with their own students (print or digital).
• Sharing, uploading, reselling, or redistributing is strictly prohibited.
• For multi-teacher or school-wide licensing, email contact@understandthemath.com