Subspaces and Span

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Now that we know what vector spaces are, let's learn about subspaces. These are smaller spaces contained within a larger vector space that are themselves vector spaces.
Script by Howard Whittle
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Опубликовано:

25 мар 2019

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Комментарии : 129

@dominiquedewet3311 5 лет назад

No professor of mine is able to compete with your brilliant explanations. Something seemingly complicated made so simple.

@damiankarsyn9653 3 года назад

i guess it is pretty randomly asking but does anyone know a good place to watch newly released series online?

@biglexica7339 2 года назад

@@damiankarsyn9653 no

@andrewkorsten2423 9 месяцев назад

@@damiankarsyn9653 what series?

@GoldenTiger01 5 месяцев назад

@@andrewkorsten2423 Fourier series?

@republicraider8336 Год назад

You've just explained in 5 minutes what took my professor four weeks to half explain. Thank you.

@alish2001 4 года назад

I literally have a midterm in 2 hours you are a godsend

@micoluk9446 2 года назад

i have a meeting with ur mom in like 2 minutes

@DARTH-R3VAN 2 года назад

@@micoluk9446 how was it

@micoluk9446 2 года назад

@@DARTH-R3VAN just like with ur mom

@tomatrix7525 2 года назад

Yup we’re fucked

@DARTH-R3VAN 2 года назад

@@tomatrix7525 like our moms

@linnsandvik6308 3 года назад

I really appreciate that you are speaking so clearly! It makes your videos easy to follow despite my hearing loss:)

@andrewkorsten2423 9 месяцев назад

I am just doing video 33. I went to the last ones to check out whether the quality is going out, or the topics are too complex. But every video has only positive comment, which are clarly not farmed. IT's clear that the series is highly effective in teaching us the bascis. I am brushing up on math overall, and it feels great to be doing this course.

@snpthompson Год назад

you are the best! i hope you continue to upload these videos because you are the best teacher i’ve had! i know that so many others you have helped would agree

@noahbarrow7979 3 года назад

this linear algebra playlist of yours is the absolute best i've come across on the internet. Thank you for being so lucid and lending so much clarity to these (sometimes) abstract concepts. Are you making a differential equations playlist? Would love to see some ODE!!

@ProfessorDaveExplains 3 года назад

Yes I've been meaning to do that for a while! Just looking for the right writer.

@tejasgowdakr4700 2 года назад

@@ProfessorDaveExplains pls do PDE also (love from india )

@thedoc6413 Год назад

@@ProfessorDaveExplainsdo you still plan on doing this?

@neham1008 Год назад

bro you are the best at teaching this. I'm sooo grateful for your videos. Thank you so much! I was stressing out like crazy for my upcoming quiz until I came upon your teaching videos.

@annaduong9830 3 года назад

I did love this vid so much. It helped me to understand the basis of vector spaces which had taken me a lot of time to learn in the class.

@zeffdronin6422 2 месяца назад

you really a gem. i cannot express enough gratitude for your videos, and im certain im not the only one to feel this way. thank you!

@arnavkanathia757 3 года назад

great professor just teaching complicating things with such ease

@enweremfavour5315 2 года назад

You have made algebra easier for me compared to our boring lecturers. Thanks a lot. Much love ❤️ from Nigeria 🇳🇬

@dikachinwankwo1935 2 года назад

Seriously 🥺

@mehmettoktas5430 3 года назад

Thanks for ur quality learning style Professor.Thanks from Turkey.

@user-yg6lf3ig2q 2 года назад

You are really explaining brillians as we are always doing right in checking comprehension

@zandertaljaard5431 2 месяца назад

Note to viewers: The vector space V (as in the video) is also a subspace of itself. Hence, S does not have to be strictly smaller than V, as Dave slightly misleadingly stated in the introduction.

@ramankumar41 Год назад

nice explanation Prof. Dave

@mdmahmudhasan1645 2 года назад

Clear explanation, carry on.

@user-fy2ud4fq4g 5 месяцев назад

5:12 what if we multiplied by a negative scalar? Would we still get a matrix in the specified form?

@mrtoys3094 3 года назад

Thank you for saving my semester professor much love from Kenyatta university ( Nairobi Kenya)

@abu-bakrmohamed1707 2 года назад

WOW , u made everything clear for me thank u so much :)

@nataliatothemoon 3 года назад

Praying Tanaka is so lucky to have found you Professor Dave.

@navaerick86 8 месяцев назад

Wish I had a professor like you

@anas8296 7 месяцев назад

in 5 minutes , you have perfectly explained what my professor failed to teach us for 4 hours, much appreciated

@PrawjektSilvia 3 месяца назад

I think it's important to note that a subspace must also contain the additive identity. In the case of vectors, it must contain the zero vector. Great video!

@Smoothcurveup52 Год назад

Wow wonderful explaination

@kalpeshyadav1391 3 года назад

Awesone very nice explanation

@HWFieldGoal 2 года назад

Thank you it is help full lecture!!!!

@honeycocoa1907 6 месяцев назад

argh thank you so much i was having a hard time understanding all this. The video is so good i had to watch it 3 time lol

@sakinsayeem419 Год назад

Can you please explain what you meant by 'Any sum of these elements" in 3:20

@user-uv3up3xe1r 26 дней назад

Thank you so much!

@joshuawang9401 3 года назад

TY professor!

@pwny4995 2 года назад

What are the difference between a Span and a Subspace?

@Abdulrahman-hb6fy 3 месяца назад

the span of any number of elements of vector V is also a subspace of V a span is the smallest subspace of V that contains this set of elements span is important for describing vector spaces

@thefrenchiestfry8147 2 года назад

For closure under addition, do the vectors that are added to vectors in a subspace have to be part of the subspace themselves?

@noone-fx8dx 2 года назад

yes

@dr.walidsoula 2 года назад

Very nice,Thx

@k_nito7954 10 месяцев назад

Hey sir! I was just wondering, can the scalar for the 1st rule of Vector Spaces be a negative? If yes, wouldn't it make the matrix in the 1st question of Checking Comprehension not a subspace? Since the -b in the bottom row would turn positive

@t.gmultiplex2838 6 месяцев назад

I'm not a professor but if you are talking about the 2bd question in last then if 2nd row if b becomes positive then b in first row will to -b thus form will remain same

@manishbhanga 4 года назад

What if c is negative?

@Christian-mn8dh Год назад

exactly what I was thinking

@arwaomer9795 Год назад

Me too😅

@endabenson701 11 месяцев назад

Think it still works cause the bottom will be positive and the top will be negative, in other words, the bottom is the negative of the top line which is negative. A bit confusing but I think the rule he stated was that the bottom line is the negative of the top line, not that the bottom line itself is necessarily negative.

@quantumleap7964 Год назад

here is an interesting idea, since points in cartesian space are just sums of the i-hat and j-hat basis vectors with real coefficients technically speaking all of the 2-d coordinates system is simply span(i_hat,j_hat). Similarily the 3-d cartesian system is just span(i_hat,j_hat,k_hat)

@josephbadana5002 4 года назад

thanK you so much.

@longvo2083 2 года назад

Why the first question of the comprehensive is true? Could someone explain it please?

@nafiurrahman722 10 месяцев назад

I didnt understand the part where span of V is the smallest subspace of V. How come? The a1V1+a2V2+a3V3 (if linearly independent) is the entire R3 right?

@simondx6694 5 лет назад

I already miss your long hair

@fishlasagna7368 5 лет назад

simon dx I agree

@gamensmpro2819 2 года назад

Thanks

@arefinsiddque6666 2 года назад

Sir, multiply vector x with any negative constant value. Then, will the resultant vector x belong to the set S?

@vigneshsenthil7980 Год назад

same doubt

@kaanylmaz1008 2 года назад

teşekkürler, iyi geldi

@johnrhodes9964 6 дней назад

i have a doubt, the video tells that the definition of linear combination is "some of all the elements of a vector space multiplied by some scalars" and the definition of span is given as "set of all possible linear combinations". but in the example, only one possible linear combination of the vector space is considered and given the name span, shouldn't the span be a set of v1 v2 and v3 multiplied by diff series of scalars, why just stop with a b and c? x(v1) + y(v2) + z(v3) should also be a linear combination of the space. and the set of V multiplied by a,b,c and x,y,z should be called a span?

@karlmax61 3 года назад

PLEASE MAKE LECTURES ON REAL ANALYSIS

@alhadibalouch8442 4 года назад

i have a midterm tomorrow thx

@JJ-pz2dx 2 месяца назад

I have a midterm in 3 hours 😩 thank you so much

@nobody48803 2 месяца назад

awesome

@Christian-mn8dh Год назад

2:20 is it really closed under scalar multiplication? what if c is negative???

@carultch Год назад

No issue if c is negative. The original vectors can be any vectors in the form of [[x],[0],[-x]], where x is any real number. The multiplier c, can also be any real number. Multiplying any two real numbers together, also gets a real number, and x*c will still be the negative of -x*c.

@qingyangzhang887 5 лет назад

Thank you so much. By definition would a vector space be a (very useless) subspace of itself?

@AEPPLE_MUSIC 2 года назад

Know it's too late but for anyone with a similar question: V is in itself a subspace of V.

@twi4458 2 года назад

@@AEPPLE_MUSIC Makes sense

@shriyanshkatiyar5807 Год назад

YES OFCOURSE! IT WOULD BE. 🙂

@zxcxdr1 2 года назад

English is my third language, and you still explain better than my professors in my mother tounge

@bouyancyyang943 2 года назад

in 5:09 (2), can their span be in real number instead of a & b?

@amartyapanwar3164 Год назад

well, you assume a and b to be constants that are also real numbers. so the span, as a result, will be a real number, as you're not dealing with any variables here...hope this helps :)

@animeparadise2461 10 месяцев назад

Sir in Example of subspace what if we take the value of scalar as negative then the 1st property will not be held . Please help me with my doubt.

@t.gmultiplex2838 6 месяцев назад

How

@BagavaanSriKrishn 10 месяцев назад

Watching 10 min before exam

@Sunny-qe5el 3 года назад

Multiplying zero scalar to a vector will yield zero result, So, in case of subspace, we could say that it is closed for scalar multiplication?

@Christian-mn8dh Год назад

c = 0 makes me think of another question. If c = 0, then the vector is [0,0,0]. which means it's not maintaining the [x,0,-x] form??? idk. pls help

@lankaputhra4825 Месяц назад

What if sub space doesn’t include identity O but satisfies closure . It’s not a vector space is it? Still a subspace? If so not every subspace is vector space. Am I missing something ?

@devendraonly239 6 месяцев назад

2:00 why we are checking its closed or not, since its a subset of vector space.. Confused!

@arvind9438 3 месяца назад

we are trying to check if it is indeed a subset , thats why

@wenanyaugustine3311 10 месяцев назад

what if you had used -1 as a scalar to multiply?

@animeparadise2461 10 месяцев назад

i am facing the same issue

@suprememaster1951 2 года назад

Every subspace of R5 that contains a nonzero vector must contain a line. Is this statement true?

@vinayakpawar2592 Месяц назад

yes!

@curtpiazza1688 4 месяца назад

Great ! Thanx! 😂

@hse2951 3 года назад

I don't understand R 2*2 Could you explained it

@johanjimenez1249 3 года назад

he made a video called understanding vector space

@carultch Год назад

The R refers to real numbers. The 2x2 refers to 2x2 square matrices. Putting it together, it refers to the set of all square matrices with 2 rows and 2 columns that contain any real number in each of the 4 entries.

@leoncraftmc 2 года назад

2:09, why is it “-(cx)”? c * (-x) is -cx

@ammyvl1 2 года назад

just to illustrate that it's some number in the form -x better

@carultch Год назад

Multiplication of real numbers is associative and commutative, so you can rearrange the parentheses and negative sign, however you prefer.

@kapjoteh 3 года назад

2:28 what if c was -1

@bigilpandi7722 3 года назад

Scalar positive integer

@multitude1337 2 года назад

@@bigilpandi7722 wrong

@multitude1337 2 года назад

c can be any real number, remember it's a scalar, so it can be negative. thus, it will still work as the first component of the x vector has the opposite sign of the third component of the x vector, so it still satisfies this closure property

@Christian-mn8dh Год назад

@@multitude1337 so what does 'form' really mean? im confused

@carultch Год назад

@@Christian-mn8dh Think of form as meaning pattern. A vector in the form of [[x],[0],[-x]] means that you can put any (real in this case) number in the position of the x, in both the first and final entry of this vector. So this means that [[4], [0], [-4]] as well as [[-6], [0], [-6]] are vectors of this form. They have something in common, in that their first and final entries are negatives of each other, and they have zero for the middle entry. Note that the nested brackets is my way of indicating the vertical matrix, in an inline text description. Think of the innermost brackets as individual rows, and the outermost bracket as the full matrix of those rows. In this case, there's just one entry per row, since vectors in linear algebra are considered vertical matrices.

@Dilshannarankotuwa Год назад

❤

@hero_of_winds7311 4 месяца назад

Can someone explain #2 to me?

@mcalkis5771 2 года назад

Why the hell am I getting "Feet finder" ads on RU-vid?? And on math tutorials of all places???

@justthenamekevin 2 года назад

french: Span is written as Vect

@syedannasali8039 Год назад

Hrs of lec

@rajanraju4194 5 лет назад

Private videos ??

@ProfessorDaveExplains 5 лет назад

they'll be released one per week

@hassannabil7309 4 месяца назад

Midterm in 20 minutes 💀💀

@vaibhavshilar7697 3 года назад

Sir Hindi

@killercat50y 2 года назад

Don't know if you will ever see this comment, but thank you. You are getting me through my college linear algebra class. My teacher is so bad at explaining things, and you make it so simple to understand.