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Joy Zhou
United States
Registrace 2. 10. 2012
Testing if a subset of a vector space is a subspace, the 2 axioms involved and why
In this video, I'll explain why we only need to test 2 axioms (among the 10 axioms in the definition of a vector space) when figuring out if a subset is a subspace.
zhlédnutí: 15 019
Video
Subspaces Part 1: definition of a subspace
zhlédnutí 3KPřed 7 lety
Preliminaries: 1. What is a subset? 2. How to verify a set is a subset of another set? 3. Notations and language of set theory related to subsets. In this video, we introduce the definition of a subspace. We go through a preliminary example to figure out what do subspaces of R^2 look like, and we will continue to talk about how to verify a subset of a vector space is a subspace in later videos.
Vector space Part 3: definition of a vector space
zhlédnutí 1,3KPřed 7 lety
The concept of a vector space is somewhat abstract, and under this definition, a lot of objects such as polynomials, functions, etc., can be considered as vectors. This video explains the definition of a general vector space. In later videos we will look at more examples.
Vector spaces Part 2: What makes R^n a "space" continued
zhlédnutí 850Před 7 lety
In this video we continue to list the properties of R^n. The 10 properties listed in this video and the previous video will be used to define a general vector space.
Vector space Part 1: what makes R^n a "space"
zhlédnutí 1,6KPřed 7 lety
This video kicks off the series of videos on vector spaces. We begin by summarizing the essential properties of R^n.
Vector operatorations: addition, subtraction, scalar multiplication, Part 2, algebraic
zhlédnutí 259Před 7 lety
In this video we learn to add, subtract, and scalar multiply vectors in an algebraic way. The take-home message is that addition, subtraction, and scalar multiplication of vectors are done component-wise.
Vector operations: addition, subtraction, & scalar multiplication, Part 1, geometric
zhlédnutí 1,1KPřed 7 lety
In this video we'll learn about the geometric approach to: 1. add two vectors; 2. subtract two vectors; 3. multiply a vector by a scalar. Take-home messages: 1. Parallelogram rule 2. Triangle rule 3. The negative of a vector 4. The zero vector
What are vectors? Part 4, the Euclidean n-space
zhlédnutí 4,7KPřed 7 lety
In this video, we introduce the Euclidean 3-space R^3 and higher dimensional Euclidean spaces, R^n. Learning objectives: 1. What is R^3? How many components does a vector in R^3 have? 2. What is R^n? Take-home messages: 1. R^3 is the set of all 3-tuples whose components are real numbers. 2. Geometrically, R^3 represents the 3-dimensional space. 3. R^n is the set of all n-tuples with real compon...
What are vectors? Part 3, components of a vector
zhlédnutí 299Před 7 lety
Learning objectives: 1. The components of a vector in R^2 whose initial point is at the origin (0,0); 2. The components of a vector in R^2 whose initial point is NOT at the origin.
What are vectors? Part 2, vectors in the xOy coordinate system
zhlédnutí 453Před 7 lety
What are vectors? Part 2, vectors in the xOy coordinate system
What are vectors? Part 1, physical and geometric vectors
zhlédnutí 551Před 7 lety
What are vectors? Part 1, physical and geometric vectors
Introduction to Matlab interface and the publishing feature (instructions for labs in MATH 272)
zhlédnutí 254Před 7 lety
This video is for MATH 272, Linear Algebra and Applications. In this video, I will give you a quick introduction to Matlab, including how to use the m-file editor, the cell-mode, and the publishing feature. Towards the end of the video, I'll talk about instructions specific to the lab sections in MATH 272.
Example of a linear equation (Breakfast series part 1)
zhlédnutí 254Před 7 lety
This is the first video in the "What to eat for breakfast?" series. In this video, we present a linear equation that is used to solve the problem "what to eat for breakfast to ensure 30 grams of protein intake".
How to verify & visualize a solution of a linear equation (Breakfast series part 2)
zhlédnutí 480Před 7 lety
This is the 2nd video in the "What to eat for breakfast?" series. In this video, we demonstrate: 1) how to verify a given ordered 2-tuple is a solution to a given linear equation; 2) how to visualize the set of solutions to a given linear equation about two unknowns in the x-O-y plane; 3) present the fact that a linear equation about two unknowns has infinitely many solutions. In fact, the set ...
What is a linear system? A 2 by 2 example. (Breakfast series part 3)
zhlédnutí 402Před 7 lety
In this video, we present an example (2 by 2) of a linear system by imposing a second linear equation in addition to the equation we had in part 1 and part 2 of the series. This is the 3rd video in the "What to eat for breakfast?" series. This video is based on some previous videos: Definition of a linear equation: czcams.com/video/BFMH58cwSKE/video.html Example of a linear equation (Part 1 of ...
What is a homogeneous linear equation? (Definition and examples)
zhlédnutí 13KPřed 7 lety
What is a homogeneous linear equation? (Definition and examples)
What is a linear system? (Definition and examples)
zhlédnutí 21KPřed 7 lety
What is a linear system? (Definition and examples)
What is a homogeneous linear system? The definition.
zhlédnutí 2,1KPřed 7 lety
What is a homogeneous linear system? The definition.
What is a linear equation? (Definition and examples)
zhlédnutí 24KPřed 7 lety
What is a linear equation? (Definition and examples)
Complex eigenvalues and eigenvectors: An Example Part 3
zhlédnutí 4,2KPřed 8 lety
Complex eigenvalues and eigenvectors: An Example Part 3
Complex eigenvalues and eigenvectors: An Example. Part 2
zhlédnutí 11KPřed 8 lety
Complex eigenvalues and eigenvectors: An Example. Part 2
Complex Eigenvectors: An Example. Part 1
zhlédnutí 15KPřed 8 lety
Complex Eigenvectors: An Example. Part 1
Complex Eigenvalues and Eigenvectors: complex conjugates
zhlédnutí 1,9KPřed 8 lety
Complex Eigenvalues and Eigenvectors: complex conjugates
Linearly independent functions: example
zhlédnutí 10KPřed 8 lety
Linearly independent functions: example
The rank nullity relation and examples
zhlédnutí 154KPřed 8 lety
The rank nullity relation and examples
How to find the range of a matrix: example
zhlédnutí 159KPřed 8 lety
How to find the range of a matrix: example
How to find the null space and the nullity of a matrix: Example
zhlédnutí 296KPřed 8 lety
How to find the null space and the nullity of a matrix: Example
You can also use gauss elimination method for this .
Nice pencil
best tutorial in 2024 EUNE
What a great video to be honest
You wok my neighbors lol
I'm so confused because in the end you say they're not linearly dependent but then immediately after you say that they are.
what if we took a3=0?
You explained the concept very well.Tomorrow is my exam,thankyou very much for the wonderful video. -- Yaipha Luwang
thank you
Thank you ❤
hap bilgi
This was the most easy to understand example present on youtube. Thank you so much
awesome videoooo
Thank you mam
finally i was able to understand this topic. but it think this is not a detailed lecture like how the values of a1,a2,a3 were found😥
This was quick and easy to understand .Thanks
The video is getting stuck at 0:09
What is she doing
You're such a poor teacher
Finally I found a single understanding video for null space.....
Simple and precise, thanks alot 🎉🎉❤
Disgusting
The video is old but the concept is taught well
Hi Joy, Thank you so much for these valuable videos, I feel like I am ready to enroll in your class. I have a question on the last part of this video where you said that in certain application that you need a symmetric matrix but how could a multiplying transpose simply symmetrize a asymmetric matrix ?
the two equation will be 1. a1 = -2a2 2. a2= a3
But it is equals when that is a square matrix
MY GOD YOUR MICCCC
Super...
This is so wrong on so many levels. Not the answers. The explanations. You are throwing people off by labeling in a horrible way. You also can't use zero as the first and only example of your work. You move on to already scaled vectors without explaining that you have done so. Just wrong. You have to explain step by step if you want to make a proper tutorial.
Your voice is sexy
hi please clear me how the rank(A transpose) = 3??
Juzakallha mam
I got a jumpscare at first, but thanks overall.
after 7years i am watching this..... but the content is still fresh. Thank u for this beautiful explanation. I hope that u are doing Great in your life Joy (◡‿◡)
I want u to put the whole mic in ur mouth so i can hear u better
Great explanation
gave me a heart attack at the beginning
You explained in 3 minutes what my professor couldn't explain in an hour. Thank you
+1
Thanks mam a lot of thanks for providing the main concept mam i have a 1 question mam is spanning set have both Linearly dependent or Linearly independent vectors ?
my brother in christ my ears are bleeding
thx joy
Row reduce Tera baap karega ?
Thank you ma'am
thanks.
*_"AAAAAAAAAA"_* "Therefore the nullity of A is two :)"
Why did you skip you waste of time
Thanks alot Sis, it helped me so much and my all concepts are clear, Bundle of thanks to you ❤️❤️
Thank you mam,take love from Bangladesh.
This kind of short videos are saviors!
7 years later: thank you ! November 2022!