Objectives of general skills

• Understand "elementary" mathematics profoundly
• Use vector spaces, linear applications and the techniques associated with them
• Understand basic algebraic structures
• Manipulate previously acquired knowledge that appears in a question
• Give examples and counterexamples for definitions, properties, theorems, etc.
• Understand and produce strict mathematical reasoning
• Write clearly and concisely
• Use mathematical vocabulary and formalism appropriately
• Make sense of formal expressions
• Rely on a picture to illustrate a concept, rationale, etc.
• Solve new problems
• Abstract and manipulate theories and use these to solve problems
• Adapt an argument to a similar situation

UE's Learning outcomes

Structure results in linear algebra: reduction of endomorphisms and spectral theory in Euclidean and Hermitian spaces.
The aim of this course is to develop the algebraic theory of endomorphism algebras of finite dimensional vector spaces, possibly endowed with a definite symmetric bilinear form.

UE Content

Diagonalisation, eigenvalue, eigenvector, characteristic polynomial, minimal polynomial, Cayley-Hamilton, Jordan form.
Duality, bilinear symmetric form, orthogonality, non-degeneracy, transpose and adjoint endomorphism, automorphism, orthogonal basis, definite form.
Euclidean and Hermitian space, norm, Cauchy-Schwarz, orthonormal basis, Gram-Schmidt, spectral theorems.

Prior experience

"Algèbre linéaire et géométrie I" course. 

Term 1 for Integrated Assessment - type

• Written examination

Term 1 for Integrated Assessment - comments

Not applicable

Term 2 for Integrated Assessment - type

• Written examination

Term 2 for Integrated Assessment - comments

Not applicable

Term 3 for Integrated Assessment - type

• Written examination

Term 3 for Integrated Assessment - comments

Not applicable

Resit Assessment for IT - Term 1 (B1BA1) - Comments

Not applicable