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Lecture

Linear Differential Equations

In course

MATH-115(a): Advanced linear algebra II - diagonalization

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet. ...

Description

This lecture covers the solution of linear differential equations, focusing on the process of finding complex solutions and the special case of diagonalizable matrices. The instructor explains the steps to follow and provides examples to illustrate the concepts.

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Instructor

Friedrich Eisenbrand

Friedrich Eisenbrand's main research interests lie in the field of discrete optimization, in particular in algorithms and complexity, integer programming, geometry of numbers, and applied optimization. He is best known for his work on efficient algorithms for integer programming in fixed dimension and the theory of cutting planes, which are an important tool to solve large scale industrial optimization problems in practice. Before joining EPFL in March 2008, Friedrich Eisenbrand was a full professor of mathematics at the University of Paderborn. Friedrich received the Heinz Maier-Leibnitz award of the German Research Foundation (DFG) in 2004 and the Otto Hahn medal of the Max Planck Society in 2001.

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related concepts (32)

Diagonalizable matrix

In linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .

Exam

An examination (exam or evaluation) or test is an educational assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics (e.g., beliefs). A test may be administered verbally, on paper, on a computer, or in a predetermined area that requires a test taker to demonstrate or perform a set of skills. Tests vary in style, rigor and requirements. There is no general consensus or invariable standard for test formats and difficulty.

Notebook interface

A notebook interface or computational notebook is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded in formatted documents; others separate calculations and text into separate sections. Notebooks share some goals and features with spreadsheets and word processors but go beyond their limited data models. Modular notebooks may connect to a variety of computational back ends, called "kernels".

Notebook

A notebook (also known as a notepad, writing pad, drawing pad, or legal pad) is a book or stack of paper pages that are often ruled and used for purposes such as note-taking, journaling or other writing, drawing, or scrapbooking. The earliest form of notebook was the wax tablet, which was used as a reusable and portable writing surface in classical antiquity and throughout the Middle Ages.

Gamma matrices

In mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts.

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