Unit · year 1

MU-103 · Linear Algebra I

Threads structure25 lectures8 theorems

Vectors, matrices, and linear maps — the language of everything linear.

PREREQUISITES

L01	Systems of Linear Equations and Gaussian Elimination —
L02	Row Echelon Form and Rank —
L03	Matrices and Matrix Algebra —
L04	The Inverse of a Matrix The invertible matrix theorem
L05	Elementary Matrices and LU Factorisation —
L06	Vector Spaces: Axioms and Examples —
L07	Subspaces, Span, and Linear Independence —
L08	Basis and Dimension —
L09	Coordinates and Change of Basis —
L10	Linear Transformations —
L11	Kernel and Image The rank–nullity theorem
L12	The Rank–Nullity Theorem The rank–nullity theorem
L13	Matrix Representation of Linear Maps —
L14	The Determinant: Definition and Properties —
L15	Cofactor Expansion and Computation —
L16	Multiplicativity of the Determinant Multiplicativity of the determinant
L17	Cramer's Rule and the Adjugate Cramer's rule
L18	The Invertible Matrix Theorem The invertible matrix theorem, Multiplicativity of the determinant
L19	Inner Products and Norms —
L20	The Cauchy–Schwarz Inequality The Cauchy–Schwarz inequality
L21	Orthogonality and Orthogonal Complements —
L22	The Gram–Schmidt Process The Gram–Schmidt process
L23	Orthogonal Matrices and QR Factorisation The Gram–Schmidt process
L24	Eigenvalues and Eigenvectors: A First Look —
L25	Synthesis: Solving, Structure, and Geometry The rank–nullity theorem, The invertible matrix theorem