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Lecture# Linear Algebra: Multilinear Forms

Description

This lecture covers the concept of multilinear forms in linear algebra, exploring their properties and applications. The instructor explains how to manipulate vectors in various ways to express multilinear forms, emphasizing their role in generating vector spaces. The lecture delves into the significance of bases and the freedom provided by multilinear forms in vector space transformations.

Official source

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In course

MATH-110(a): Advanced linear algebra I

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 (162)

Instructors (2)

DEC Alpha

Alpha (original name Alpha AXP) is a 64-bit reduced instruction set computer (RISC) instruction set architecture (ISA) developed by Digital Equipment Corporation (DEC). Alpha was designed to replace 32-bit VAX complex instruction set computers (CISC) and to be a highly competitive RISC processor for Unix workstations and similar markets. Alpha is implemented in a series of microprocessors originally developed and fabricated by DEC.

DEC 7000 AXP and DEC 10000 AXP

The DEC 7000 AXP and DEC 10000 AXP are a series of high-end multiprocessor server computers developed and manufactured by Digital Equipment Corporation, introduced on 10 November 1992 (although the DEC 10000 AXP was not available until the following year). These systems formed part of the first generation of systems based on the 64-bit Alpha AXP architecture and at the time of introduction, ran Digital's OpenVMS AXP operating system, with DEC OSF/1 AXP available in March 1993.

DEC 3000 AXP

DEC 3000 AXP was the name given to a series of computer workstations and servers, produced from 1992 to around 1995 by Digital Equipment Corporation. The DEC 3000 AXP series formed part of the first generation of computer systems based on the 64-bit Alpha AXP architecture. Supported operating systems for the DEC 3000 AXP series were DEC OSF/1 AXP (later renamed Digital UNIX) and OpenVMS AXP (later renamed OpenVMS).

DEC 4000 AXP

The DEC 4000 AXP is a series of departmental server computers developed and manufactured by Digital Equipment Corporation introduced on 10 November 1992. These systems formed part of the first generation of systems based on the 64-bit Alpha AXP architecture and at the time of introduction, ran Digital's OpenVMS AXP or OSF/1 AXP operating systems. The DEC 4000 AXP was succeeded by the end of 1994 by the AlphaServer 2000 and 2100 departmental servers.

DEC RADIX 50

RADIX 50 or RAD50 (also referred to as RADIX50, RADIX-50 or RAD-50), is an uppercase-only character encoding created by Digital Equipment Corporation (DEC) for use on their DECsystem, PDP, and VAX computers. RADIX 50's 40-character repertoire (050 in octal) can encode six characters plus four additional bits into one 36-bit machine word (PDP-6, PDP-10/DECsystem-10, DECSYSTEM-20), three characters plus two additional bits into one 18-bit word (PDP-9, PDP-15), or three characters into one 16-bit word (PDP-11, VAX).

Related lectures (490)

Linear Algebra: Multilinear FormsMATH-110(a): Advanced linear algebra I

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Linear Algebra: Bases and SpacesMATH-111(e): Linear Algebra

Covers linear independence, bases, and spaces in linear algebra, emphasizing kernel and image spaces.

Vector Spaces: Subspaces and Bases

Covers subspaces, bases, linear independence, and dimensionality in vector spaces.

Vector Spaces: Axioms and ExamplesMATH-111(e): Linear Algebra

Covers the axioms and examples of vector spaces, including matrices and polynomials.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.