Linear Algebra

Tutorial chapters

Chapters are structured to build understanding step by step, minimizing logic gaps and emphasizing geometric insight.

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Chapters

Echelon form, pivots, rank and what the algorithm reveals

Linear equations

Solve A x = b and interpret solutions structurally

Linear transformation

From matrices to geometry and back

Definition, existence, uniqueness and computation

Scaling factor and structure via row operations

Schur complement

Block matrices and elimination in matrix form

Matrix multiplication

Meaning, computation and interpretation

The four subspaces

Row, column, null and left-null spaces

Matrix shape, rank and what is / isn’t solvable