Course contents25 available

Course Linear Algebra ★The Language of Mathematics

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6 soon

L21Vector spaces
L22Subspaces, sums and intersections
L23Basis and dimension in general
L24Direct sums
R6Recitation 6

Week 7 soon

L25Coordinates
L26Row space and rank
L27The four fundamental subspaces
L28Change of basis
R7Recitation 7

Week 8 soon

L29Linear maps
L30The rank–nullity theorem
L31Isomorphisms and the space of maps
L32The matrix of a linear map
R8Recitation 8

Week 9 soon

L33Determinant as signed volume
L34The determinant defined
L35Computing determinants
L36Determinants and invertibility
R9Recitation 9

Week 10 soon

L37Eigenvalues and eigenvectors
L38The characteristic polynomial
L39Diagonalisation
L40Eigenvalues in action
R10Recitation 10

Week 11 soon

L41Complex eigenvalues
L42Invariant subspaces
L43Polynomials of matrices
L44The minimal polynomial
R11Recitation 11

Week 12 soon

L45Inner product spaces
L46Orthogonality and projections
L47Gram–Schmidt and QR
L48Least squares
R12Recitation 12

Week 13 soon

L49The spectral theorem
L50Quadratic forms
L51Singular value decomposition
L52The SVD in action and what comes next
R13Recitation 13

Before you start · Notation primer· 12:11

The Language of Mathematics

Sets and elements, set-builder notation, quantifiers, implications, functions and sums, and how mathematics is written: definition, theorem, proof. Everything the course takes for granted, in one short video and an eight-page sheet.

Video: coming soon

The primer (12:11) is not published yet. It will play right here as soon as it is on YouTube.

In this video

Why a language
Sets and elements
Building sets with a rule
Comparing and combining sets
For all, there exists, implies
Functions and sums
How mathematics is written

Materials

The notation primerwith a one-page quick reference · PDF · 8 pages · 501 KB

Then start the course with Lecture 1.