Syllabus

LEARNING OUTCOMES

You will learn about norms and inner products in infinite-dimensional vector spaces. Related to these structures, you will understand basic properties of bounded linear operators and duality in Hilbert spaces, together with diagonalization of compact self-adjoint operators.

Credits: 5

Schedule: 07.09.2022 - 17.10.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Ville Turunen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Orthogonality, orthonormal bases, bounded linear operators, functionals, and elementary spectral theory in Hilbert spaces. (Jordan-von Neuman Theorem, Riesz Hilbert Space Representation Theorem, diagonalization of compact self-adjoint operators, Hilbert-Schmidt Spectral Theorem, Singular Value Decomposition).

Assessment Methods and Criteria

• valid for whole curriculum period:

  Weekly exercises (1/3) and an exam (2/3). Alternatively, just exam (100%).

Workload

• valid for whole curriculum period:

  Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca 100h.

DETAILS

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 Autumn I
  2023-2024 Autumn I

  Enrollment :

  Registration take place in Sisu (sisu.aalto.fi).

Description