ویدیوهای Essence of linear algebra

Matrix multiplication as composition  Essence of linear algebra, chapter 4
48 بازدیدMultiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you'r

Nonsquare matrices as transformations between dimensions  Essence of linear alg
202 بازدیدBecause people asked, this is a video briefly showing the geometric interpretation of nonsquare matrices as linear transformations that go between dimensions. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you'r

The determinant  Essence of linear algebra, chapter 5
44 بازدیدThe determinant of a linear transformation measures how much areas/volumes change during the transformation. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and

Inverse matrices, column space and null space  Essence of linear algebra, chapt
20 بازدیدHow to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank and null space, but the computation of those constructs is not discussed. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new v

Dot products and duality  Essence of linear algebra, chapter 7
39 بازدیدDot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube,

Cross products  Essence of linear algebra, Chapter 8
57 بازدیدThis covers the main geometric intuition behind the 2d and 3d cross products. *Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead. It makes no difference for the result, since the determinant is unchanged after a transpose, but given how I've framed most of this series I think it is more intuitive to go with a columncentric approach. Watch the full "Essence of linear algebra" pla

Cross products in the light of linear transformations  Essence of linear algebr
107 بازدیدFor anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation. *Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead. It makes no difference for the result, since the deter

Change of basis  Essence of linear algebra, chapter 9
24 بازدیدHow do you translate back and forth between coordinate systems that use different basis vectors? Watch the full "Essence of linear algebra" playlist here: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Eigenvectors and eigenvalues  Essence of linear algebra, chapter 10
64 بازدیدA visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more,

Abstract vector spaces  Essence of linear algebra, chapter 11
115 بازدیدThe tools of linear algebra are extremely general, applying not just to the familiar vectors that we picture as arrows in space, but to all sorts of mathematical objects, like functions. This generality is captured with the notion of an abstract vector space. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want t

Essence of linear algebra preview
68 بازدیدThis introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive noti

Vectors, what even are they?  Essence of linear algebra, chapter 1
22 بازدیدI imagine many viewers are already familiar with vectors in some context, so this video is intended both as a quick review of vector terminology, as well as a chance to make sure we're all on the same page about how specifically to think about vectors in the context of linear algebra. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the dri

Linear combinations, span, and basis vectors  Essence of linear algebra, chapte
66 بازدیدThe fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several vectors and adding them together. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to rec

Linear transformations and matrices  Essence of linear algebra, chapter 3
90 بازدیدMatrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're

Threedimensional linear transformations  Essence of linear algebra, footnote
65 بازدیدWhat do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb  3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the be