Linear Algebra
The Mathematics of Vectors and Transformations
A complete journey through vector spaces, matrices, transformations, eigenvalues, and the spectral theorem.
Foundations
Vectors & Vector Spaces
The bedrock of linear algebra — vectors, spaces, and the fundamental structures that define linearity.
Matrices & Operations
The Algebra of Arrays
Rectangular arrays of numbers and their algebraic manipulations — the computational heart of linear algebra.
Linear Transformations
Functions Between Spaces
Maps that preserve the linear structure — the conceptual bridge between algebra and geometry.
Eigenvalues & Diagonalization
The Spectral Perspective
Special directions and scaling factors that reveal the intrinsic structure of linear transformations.
Inner Products & Orthogonality
Geometry in Vector Spaces
Angles, lengths, and perpendicularity in abstract spaces — bringing geometry to algebra.
Spectral Theorem & Applications
The Ultimate Diagonalization
When matrices become diagonal — the pinnacle of linear algebra with profound applications.
Matrix Decompositions
Breaking Down Complexity
Factoring matrices into simpler, more revealing components — the key to computational efficiency.
Determinants & Advanced Topics
Volume and Beyond
The measure of transformation and advanced concepts that complete the linear algebra landscape.
Guided instruction and research mentorship are offered separately → hbar.work