Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Linear Algebra: Injections, Surjections, Bijections

Description

This lecture covers the concepts of injections, surjections, and bijections in linear algebra. It explains the properties of these functions and provides examples to illustrate their applications in mathematics. The lecture also delves into the importance of understanding these concepts in various mathematical contexts.

Official source

Related concepts (32)

Mathematics

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.

Bijection, injection and surjection

In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function : The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain.

File system

In computing, a file system or filesystem (often abbreviated to fs) is a method and data structure that the operating system uses to control how data is stored and retrieved. Without a file system, data placed in a storage medium would be one large body of data with no way to tell where one piece of data stopped and the next began, or where any piece of data was located when it was time to retrieve it. By separating the data into pieces and giving each piece a name, the data are easily isolated and identified.

File format

A file format is a standard way that information is encoded for storage in a . It specifies how bits are used to encode information in a digital storage medium. File formats may be either proprietary or free. Some file formats are designed for very particular types of data: PNG files, for example, store bitmapped using lossless data compression. Other file formats, however, are designed for storage of several different types of data: the Ogg format can act as a container for different types of multimedia including any combination of audio and video, with or without text (such as subtitles), and metadata.

File descriptor

In Unix and Unix-like computer operating systems, a file descriptor (FD, less frequently fildes) is a process-unique identifier (handle) for a or other input/output resource, such as a pipe or network socket. File descriptors typically have non-negative integer values, with negative values being reserved to indicate "no value" or error conditions. File descriptors are a part of the POSIX API.

Related lectures (28)

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

R Programming: Conditions, Loops, Functions & Graphics

Covers conditions, loops, functions, and graphics in R programming with practical examples.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Definitions and Notations MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the definitions and notations related to functions.

Function Properties: Injective, Surjective, Bijective