Summation notation : shifting indices, linearity and double sums;
Complex numbers 1 : conjugates, modulus, real and imaginary parts, 3 useful identities, Argand diagram
Complex numbers 2 : Euler's formula, Polar form, De Moivre's Theorem and Trigonometric identities
Basic Arithmetic of Vectors : Additions and Scalar Multiplications, Linear Span of Real Vectors
Linear Span of (Complex) Vectors, Equations of lines in R^3,
Introduction to Vectors Spaces : Examples
More on Vectors Spaces : Examples and Non-examples,
Subspaces : (1) Closure under addition (2) Closure under scalar multiplication,
Skill: Determining subspaces of R^n,
Linear Independence I : Definition and Examples
Linear maps : examples from R^n and polynomial spaces
Correspondence between linear maps and matrices
Echelon form of a matrix : Examples & non-examples
Applications 1 : System of equations, Applications 2 : Invertibility of matrices
Criterion of unique solutions / infinitely many solutions / no solutions (Square case)
REF of matrices : Computing the inverse of a square matrix
Consistency criterion for general system
Mastering the principle of linearity
TFAE for square matrices Ver 2
A brief review on elementary matrices
Computing rank and image,
Computing nullity and kernel,
Relation with injectivity and surjectivity,
Rank and nullity theorem,
Many Extra Examples.
Determinants 1 : Cofactor expansion,
Determinants 2 : Row operations,
Properties of determinants, Common misconception,
TFAE for square matrices Ver Final,
More examples