Basis and Dimension

Share this & earn $10
Professor Dave Explains
Published at : 20 Nov 2021
88023 views
1860
47

Now we know about vector spaces, so it’s time to learn how to form something called a basis for that vector space. This is a set of linearly independent vectors that can be used as building blocks to make any other vector in the space. Let’s take a closer look at this, as well as the dimension of a vector space, and what that means.

Script by Howard Whittle

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► ProfessorDaveExplains@gmail.com
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT

linear algebravector spacesvector basis

100 Years of Earrings | Glamour

100 Years of Earrings | Glamour

Prince Family   Now We Up Lyrics

Prince Family Now We Up Lyrics

DA PUMP / U.S.A.

DA PUMP / U.S.A.

Pandemic, hot weather linked to increase in drownings

Pandemic, hot weather linked to increase in drownings

Doja Cat - Woman

Doja Cat - Woman

Why do we have hair in such random places? - Nina G. Jablonski

Why do we have hair in such random places? - Nina G. Jablonski

Wiz Khalifa - The Thrill [Official Audio]

Wiz Khalifa - The Thrill [Official Audio]

Pliage de serviette en papier fleur de lotus - LaBelleAdresse

Pliage de serviette en papier fleur de lotus - LaBelleAdresse

Aiding and Abetting | Legal Definition & Analysis | Sentencing, Defenses | George Floyd

Aiding and Abetting | Legal Definition & Analysis | Sentencing, Defenses | George Floyd

Young MC - Know How

Young MC - Know How

SOMETHING appeared to be PARKED in the daytime sky!

SOMETHING appeared to be PARKED in the daytime sky!

15 Pets That Saw Something Their Owners Couldn't See

15 Pets That Saw Something Their Owners Couldn't See

Surja el Bekare

Surja el Bekare

What is Electric Current?

What is Electric Current?

Nico Daws, Tomas Tatar, and Coach Lindy Ruff ahead of the Devils - Sabres matchup Saturday

Nico Daws, Tomas Tatar, and Coach Lindy Ruff ahead of the Devils - Sabres matchup Saturday

Eben- Without borders

Eben- Without borders

Queens Of The Stone Age - Go With The Flow (Official Music Video)

Queens Of The Stone Age - Go With The Flow (Official Music Video)

What job or activity do you normally associate with jerks? (r/AskReddit)

What job or activity do you normally associate with jerks? (r/AskReddit)

Should We Be Concerned About the Effects of Ochratoxin?

Should We Be Concerned About the Effects of Ochratoxin?

Cheryl - Let You (Official Video)

Cheryl - Let You (Official Video)

What Is Evaluation

What Is Evaluation

"손!" 했더니 '머리'를 주는 고양이🤣

"손!" 했더니 '머리'를 주는 고양이🤣

Ten in the Bed | CoComelon Nursery Rhymes & Kids Songs

Ten in the Bed | CoComelon Nursery Rhymes & Kids Songs

Three Hundredth - Killing The Messenger

Three Hundredth - Killing The Messenger

GOD SAYS THERE ARE 11 EVENTS COMING IN THE LAST DAYS

GOD SAYS THERE ARE 11 EVENTS COMING IN THE LAST DAYS

Hit & Miss - Trailer

Hit & Miss - Trailer

JUBILATION IN BIAFRALAND AS RUSSIA GOVT JOINS US & UK GOVT TO DEMAND FOR RELEASE OF MNK AND BIAFRA..

JUBILATION IN BIAFRALAND AS RUSSIA GOVT JOINS US & UK GOVT TO DEMAND FOR RELEASE OF MNK AND BIAFRA..

How to Sign Up for ROBLOX

How to Sign Up for ROBLOX

English Grammar Lesson : Difference Between "A Number Of" AND "The Number Of"

English Grammar Lesson : Difference Between "A Number Of" AND "The Number Of"

The Truth About Privatization | Robert Reich

The Truth About Privatization | Robert Reich

How to Make Doll Dress from Balloon 🎀 Parenting Hacks For Smart Moms and Dads

How to Make Doll Dress from Balloon 🎀 Parenting Hacks For Smart Moms and Dads

⚠️ SIMPLE HAIRSTYLES FOR EVERYDAY ⚠️ - Hair Tutorials

⚠️ SIMPLE HAIRSTYLES FOR EVERYDAY ⚠️ - Hair Tutorials

Amber vs. Esther: Round 2? | The Challenge: Aftermath

Amber vs. Esther: Round 2? | The Challenge: Aftermath

Christ is Sufficient - Madison Pritt, Lincoln Pritt, Clayton Rash, Caroline Rash

Christ is Sufficient - Madison Pritt, Lincoln Pritt, Clayton Rash, Caroline Rash

Kids Copy SQUID GAME! They LEARN A VALUABLE LESSON... | SAMEER BHAVNANI

Kids Copy SQUID GAME! They LEARN A VALUABLE LESSON... | SAMEER BHAVNANI

Piper Rockelle - Yesterday (Official Music Video) **EMOTIONAL** 🎸

Piper Rockelle - Yesterday (Official Music Video) **EMOTIONAL** 🎸

Sting - Shape of My Heart (Official Music Video)

Sting - Shape of My Heart (Official Music Video)

The Kulture Study: Golden Child 'DDARA' MV REACTION & REVIEW

The Kulture Study: Golden Child 'DDARA' MV REACTION & REVIEW

Math Videos:  How To Learn Basic Arithmetic Fast - Online Tutorial Lessons

Math Videos: How To Learn Basic Arithmetic Fast - Online Tutorial Lessons

Meghan Trainor - Me Too

Meghan Trainor - Me Too

Massive Attack - Karmacoma

Massive Attack - Karmacoma

How to make vehicle hose pipes in a local factory | amazing thing technology |

How to make vehicle hose pipes in a local factory | amazing thing technology |

Russ - BANKRUPT (Official Video)

Russ - BANKRUPT (Official Video)

Searching for Greta - World Premiere

Searching for Greta - World Premiere

Emily Browning - Musician, Please Take Heed (God Help the Girl)

Emily Browning - Musician, Please Take Heed (God Help the Girl)

Cliff Richard - Constantly (Cliff And The Shadows, 15.07.1964)

Cliff Richard - Constantly (Cliff And The Shadows, 15.07.1964)

Why You Should Not Help Other People

Why You Should Not Help Other People

Which Restroom Should Wolfoo Go to? - Kids Stories About Potty Training With Wolfoo | Wolfoo Family

Which Restroom Should Wolfoo Go to? - Kids Stories About Potty Training With Wolfoo | Wolfoo Family

I TRIED TO BREAK THE *STEAMPUNK CHEST* WITH A BIG MASKOT AND THIS HAPPENED..(Roblox Pet Simulator X)

I TRIED TO BREAK THE *STEAMPUNK CHEST* WITH A BIG MASKOT AND THIS HAPPENED..(Roblox Pet Simulator X)