**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Linear Algebra: Orthogonal Bases and Hermitian Forms

Description

This lecture covers the concepts of orthogonal bases and Hermitian forms in linear algebra, including the Gram-Schmidt process and the procedure for finding orthogonal bases in the case of a Hermitian space.

Login to watch the video

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

MATH-115(a): Advanced linear algebra II

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.

Related concepts (84)

Related lectures (18)

Stone Age

The Stone Age was a broad prehistoric period during which stone was widely used to make stone tools with an edge, a point, or a percussion surface. The period lasted for roughly 3.4 million years and ended between 4,000 BC and 2,000 BC, with the advent of metalworking. Though some simple metalworking of malleable metals, particularly the use of gold and copper for purposes of ornamentation, was known in the Stone Age, it is the melting and smelting of copper that marks the end of the Stone Age.

Iron Age

The Iron Age is the final epoch of the three-age division of the prehistory and protohistory of humanity. It was preceded by the Stone Age (Paleolithic, Mesolithic, Neolithic) and the Bronze Age. The concept has been mostly applied to Iron Age Europe and the Ancient Near East, but also, by analogy, to other parts of the Old World. It is also considered the third phase, of three, in the Metal Ages. The duration of the Iron Age varies depending on the region under consideration. It is defined by archaeological convention.

Bronze Age

The Bronze Age is a historic period, lasting approximately from 3300 BC to 1200 BC, characterized by the use of bronze, the presence of writing in some areas, and other early features of urban civilization. The Bronze Age is the second principal period of the three-age system proposed in 1836 by Christian Jürgensen Thomsen for classifying and studying ancient societies and history. It is also considered the second phase, of three, in the Metal Ages.

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.

Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Set Theory: Operations and Functions

Covers set theory operations, functions, and their properties such as injective, surjective, and bijective functions.

Sets & Functions: Basics

Covers the basics of sets and functions, including set operations and function properties.

Quantum Random Number Generation

Explores quantum random number generation, discussing the challenges and implementations of generating good randomness using quantum devices.

Limit of a Sequence

Explores the limit of a sequence and its convergence properties, including boundedness and monotonicity.