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# Cours scientifiques - MAA206 : Euclidean and Hermitian Spaces

## Descriptif

Euclidean and Hermitian Spaces continues the study of linear maps between vector spaces, started in MAA101. The goal is to obtain simple and efficient models for these applications up to suitable changes of coordinates. The concept of duality is initially introduced in the general context of mere vector spaces. Then, the focus is put on vector spaces enjoying a richer structure, namely prehilbert spaces, which is available in most applications (e.g. in solid mechanics or in quantum mechanics). The geometry of these spaces, as well as their important transformations (e.g. normal or unitary maps) is also discussed.

## Pour les étudiants du diplôme Programmes d'échange internationaux

Vous devez avoir validé l'équation suivante : UE MAA201

## Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vous devez avoir validé l'équation suivante : UE MAA201

Numérique sur 20

## Pour les étudiants du diplôme Programmes d'échange internationaux

### Vos modalités d'acquisition :

● Sans document

EXAM MODALITIES

The final exam, make-up exam, and remedial exam are written exams lasting 2 hours, or 2 hours and 40 minutes if you have been granted additional time.

You are not authorized to bring with you any notes, slides, calculator, device, etc.
Only a pen or a pencil is authorized.

AUTHORIZED MATERIAL FOR EXAM

Notes, slides, calculators, devices, etc, are not authorized.
Only pens are allowed.

Grades in MAA206 are determined by your performance on two short tests, the midterm exam, and the final exam.

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Each test and exam is graded on a scale from 0 to 100.

1) The grade from the final exam
2) 70% of the average of the grades from the midterm and final exams, plus 30% of the average of the grades from Test 1 and Test 2

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Your final grade will be converted into a letter grade, using a scale no less generous than the one provided in Moodle.

JUSTIFIED ABSENCE

If you are justifiably absent from the final exam, you may take a make-up exam.

If you are absent from Test 1, Test 2, or the Midterm, you have two options: you may choose to do nothing, which will not affect your final grade since it is computed from the highest score.
This means the final exam could weigh more heavily in your final grade calculation.

Alternatively, you may take part of the make-up exam to compensate:
- 50% for Test 1,
- 75% for the Midterm,
- 50% for Test 2

provided you are not making up for the final exam at the same time.

You can make up for:

- The final exam,
- Test 1, Test 2, or the midterm exam,
- Test 1 and Test 2 simultaneously.

Note: In this case, Test 1 and Test 2 will not be multiple-choice questions but will consist of standard exam problems.

Le rattrapage est autorisé (Max entre les deux notes écrêté à une note seuil)

## Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)
L'UE est acquise si Note finale >= 10
• Crédits ECTS acquis : 5 ECTS

La note obtenue rentre dans le calcul de votre GPA.