**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# Matrix Representations of Linear Applications

Description

This lecture covers the matrix representations of linear applications, focusing on the transition matrices between different bases and the concept of change of basis. It also explores examples illustrating the calculation of matrices in different bases and the characterization of linear applications through matrices. The lecture concludes with a discussion on invariants and the extraction of the kernel and image of a matrix.

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.

Related concepts (200)

Physical layer

In the seven-layer OSI model of computer networking, the physical layer or layer 1 is the first and lowest layer: the layer most closely associated with the physical connection between devices. The physical layer provides an electrical, mechanical, and procedural interface to the transmission medium. The shapes and properties of the electrical connectors, the frequencies to broadcast on, the line code to use and similar low-level parameters, are specified by the physical layer.

Network layer

In the seven-layer OSI model of computer networking, the network layer is layer 3. The network layer is responsible for packet forwarding including routing through intermediate routers. The network layer provides the means of transferring variable-length network packets from a source to a destination host via one or more networks. Within the service layering semantics of the OSI (Open Systems Interconnection) network architecture, the network layer responds to service requests from the transport layer and issues service requests to the data link layer.

Link layer

In computer networking, the link layer is the lowest layer in the Internet protocol suite, the networking architecture of the Internet. The link layer is the group of methods and communications protocols confined to the link that a host is physically connected to. The link is the physical and logical network component used to interconnect hosts or nodes in the network and a link protocol is a suite of methods and standards that operate only between adjacent network nodes of a network segment.

Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

Related lectures (1,000)

Matrix Representations of Linear Applications

Covers matrix representations of linear applications in R³ and the invariance of rank.

Linear Applications: Vectorial Structure

Explores the vectorial structure of linear applications, including addition, scalar multiplication, and matrix representation.

Vector Spaces in R2 and R3

Covers vector spaces in R2 and R3, including examples of proportional families and coordinate transformations.

Linear Applications Overview

Covers the definition of linear applications and their properties, including examples and matrix representation.

Characteristic Polynomials and Similar MatricesMATH-111(e): Linear Algebra

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.