Course unit, curriculum year 2023–2024
MATH.MA.140
Vektorit ja matriisit, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
Course code
MATH.MA.140Language of instruction
englanti, suomiAcademic years
2021–2022, 2022–2023, 2023–2024Level of study
PerusopinnotGrading scale
Yleinen asteikko, 0-5Persons responsible
Vastuuopettaja:
Simo Ali-LöyttyVastuuopettaja:
Terhi KaarakkaVastuuopettaja:
Jussi KangasVastuuopettaja:
Philipp MüllerVastuuopettaja:
Tanja PalmrothVastuuorganisaatio
Informaatioteknologian ja viestinnän tiedekunta 100 %
Järjestävä organisaatio
Tietotekniikan opetus 100 %
Ydinaines
Lineaariset yhtälöryhmät ja näiden ratkaisu Gaussin eliminoinnilla,
euklidisen avaruuden vektorijoukon lineaarinen riippumattomuus,
euklidisen avaruuden aliavaruus, kanta
ja dimensio,
suorat ja tasot,
matriisit, neliömatriisin determinantti, ominaisarvot ja diagonalisointi,
vektorien pistetulo, ristitulo ja vektorikolmitulo.
Täydentävä tietämys
Learning outcomes
Prerequisites
Further information
Learning material
Equivalences
Kokonaisuudet, joihin opintojakso kuuluu
Completion option 1
Suoritustapa sisältää sellaiset opetuksen toteutukset, joissa arviointi ei sisällä tenttiä. Suoritustapa ei tarjolla lukuvuonna 2022-2023.
Osallistuminen opetukseen
No scheduled teaching
Completion option 2
This completion method is for English language implementations.
Completion of all options is required.
Osallistuminen opetukseen
28.08.2023 – 15.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Tentti
14.10.2023 – 29.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
23.10.2023 – 03.12.2023
Active in period 2 (23.10.2023–31.12.2023)
25.11.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
21.12.2023 – 31.12.2023
Active in period 2 (23.10.2023–31.12.2023)
08.12.2023 – 19.12.2023
Active in period 2 (23.10.2023–31.12.2023)
04.11.2023 – 16.11.2023
Active in period 2 (23.10.2023–31.12.2023)
01.02.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
03.01.2024 – 16.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
06.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
11.03.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
24.04.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
08.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 3
Periodi 2: Flippaustoteutus on tarkoitettu kaikille ensimmäisen vuoden opiskelijoille.
Completion of all options is required.
Osallistuminen opetukseen
23.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
Tentti
14.10.2023 – 29.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
23.10.2023 – 03.12.2023
Active in period 2 (23.10.2023–31.12.2023)
25.11.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
21.12.2023 – 31.12.2023
Active in period 2 (23.10.2023–31.12.2023)
08.12.2023 – 19.12.2023
Active in period 2 (23.10.2023–31.12.2023)
04.11.2023 – 16.11.2023
Active in period 2 (23.10.2023–31.12.2023)
01.02.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
03.01.2024 – 16.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
06.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
11.03.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
24.04.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
08.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 4
Suoritustapa ei tarjolla lukuvuonna 2022-2023.
Completion of all options is required.
Osallistuminen opetukseen
No scheduled teaching
Tentti
14.10.2023 – 29.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
23.10.2023 – 03.12.2023
Active in period 2 (23.10.2023–31.12.2023)
25.11.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
21.12.2023 – 31.12.2023
Active in period 2 (23.10.2023–31.12.2023)
08.12.2023 – 19.12.2023
Active in period 2 (23.10.2023–31.12.2023)
04.11.2023 – 16.11.2023
Active in period 2 (23.10.2023–31.12.2023)
01.02.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
03.01.2024 – 16.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
06.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
11.03.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
24.04.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
08.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 5
Verkkosuoritustavan opetus tapahtuu pääosin etäopetuksena. Opetuksen tukitoimia järjestetään kuitenkin osittain myös lähiopetuksena.
Completion of all options is required.
Tentti
14.10.2023 – 29.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
23.10.2023 – 03.12.2023
Active in period 2 (23.10.2023–31.12.2023)
25.11.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
21.12.2023 – 31.12.2023
Active in period 2 (23.10.2023–31.12.2023)
08.12.2023 – 19.12.2023
Active in period 2 (23.10.2023–31.12.2023)
04.11.2023 – 16.11.2023
Active in period 2 (23.10.2023–31.12.2023)
01.02.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
03.01.2024 – 16.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
06.05.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
11.03.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
24.04.2024 – 05.05.2024
Active in period 4 (4.3.2024–31.5.2024)
20.05.2024 – 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
08.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Osallistuminen opetukseen
28.08.2023 – 10.12.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
08.01.2024 – 30.04.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
08.01.2024 – 28.04.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
13.05.2024 – 31.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)