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Course, academic year 2018/2019
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Linear Algebra and Geometry 1 - NMAG101
Title in English: Lineární algebra a geometrie 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1819
Guarantor: doc. Mgr. Libor Barto, Ph.D.
Mgr. Dalibor Šmíd, Ph.D.
Class: M Bc. FM
M Bc. FM > Povinné
M Bc. FM > 1. ročník
M Bc. MMIB
M Bc. MMIB > Povinné
M Bc. MMIB > 1. ročník
M Bc. MMIT
M Bc. MMIT > Povinné
M Bc. OM
M Bc. OM > Povinné
M Bc. OM > 1. ročník
Classification: Mathematics > Algebra
Incompatibility : NALG001
Interchangeability : NALG001
Is co-requisite for: NMAG102
Is pre-requisite for: NMNM331
In complex pre-requisite: NMAG201, NMAG202, NMFM202, NMSA336
Annotation -
Last update: G_M (15.05.2012)
The first introductory lecture in linear algebra for General Mathematics, Financial Mathematics, and Information Security. Basic matrix operations, systems of linear equations, arithmetic vector spaces, linear dependence, linear envelope, dimension, orthogonality and orthogonalization, matrix decompositions, least squares problem, determinants.
Course completion requirements - Czech
Last update: Mgr. Dalibor Šmíd, Ph.D. (22.10.2018)

Zápočet z předmětu je nutnou podmínkou účasti u zkoušky.

Podmínkou pro získání zápočtu je zisk dostatečného počtu bodů za kvízy a domácí úkoly v průběhu semestru, podrobně jsou podmínky popsány na stránce k přednášce http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1819. Povaha kontroly studia pro získání zápočtu vylučuje možnost opakování této kontroly.

Literature -
Last update: doc. RNDr. Jiří Tůma, DrSc. (22.05.2017)

C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM 2000.

T.S. Blyth, E.F. Robertson, Basic Linear Algebra, Springer Verlag London,2002,

S.H. Friedberg, A.J. Insel, L.E.Spence, Linear Algebra, Third Edition, Prentice-Hall, Inc., 1997

L. Barto, J. Tůma, Lineární algebra a geometrie, elektronická skripta

Requirements to the exam - Czech
Last update: Mgr. Dalibor Šmíd, Ph.D. (22.10.2018)

Zkouška je písemná, podrobné informace a požadavky jsou na stránce přednášky http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1819 .

Syllabus -
Last update: doc. RNDr. Jiří Tůma, DrSc. (11.10.2017)
  • fields, characteristic of a field,
  • systems of linear equations, Gauss elimination, parametric form of the solution set
  • elements of matrix operations, matrix as a linear mapping, group of regular matrices
  • abstract vector spaces, linear independence, linear span, basis, dimension, rank of a matrix, fundamental subspaces of a matrix,
  • linear mapping, matrix of a linear mapping, change of basis, space of linear mappings,
  • determinant, geometric meaning, Vandermond matrix

 
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