Here is an infinite-dimensional version of Euclidean space: In the space of all infinite sequences, consider the subspace ℓ2 of square-summable sequences [i.e., those sequences (x1, x2, …) for which the infinite series x1^2 .x2^2 ⋯ converges ] . For x⃗ and y⃗ in ℓ2, we define x⃗=√(x1^2 x2^2 ⋯), x⃗ ·y⃗=x1 y1 x2 y2 ⋯(Why does the series x1 y1 x2 y2 ⋯converge?) a. Check that x⃗=(1, (1)/(2), (1)/(4), (1)/(8), (1)/(16), …) is in ℓ2, and find x⃗. Recall the formula for the geometric series: 1 a a^2
numerade.com
Here is an infinite-dimensional version of Euclidean space: In the space of all infinite sequences, consider the subspace ℓ2 of square-summable sequences [i.e., those sequences (x1,
VIDEO ANSWER: Here is an infinite-dimensional version of Euclidean space: In the space of all infinite sequences, consider the subspace \ell_{2} of square-summ…
2023年1月27日
Infinite Universe Theory
Ever wondered if our universe is just one of many? 🌠 'Unlocking the Infinite Possibilities: Exploring the Mind-blowing Multiverse Theory' takes you on a journey through this fascinating concept. #multiverse #SpaceMysteries | Cosmo-facts
0:54
Ever wondered if our universe is just one of many? 🌠 'Unlocking the Infinite Possibilities: Exploring the Mind-blowing Multiverse Theory' takes you on a journey through this fascinating concept. #multiverse #SpaceMysteries | Cosmo-facts
FacebookCosmo-facts
已浏览 6089 次2023年12月8日
What Is the Multiverse Theory? | Infinite Universes Explained
1:27
What Is the Multiverse Theory? | Infinite Universes Explained
YouTubeWhat Is
已浏览 612 次2 个月之前
916K views · 9.1K reactions | One of the most important is that Einstein's theory incorporates the cosmic speed limit: the speed of light. Newton had assumed that gravity is felt everywhere in the Universe instantaneously, in other words that it travels at infinite speed. | The Science of Universe | Facebook
0:55
916K views · 9.1K reactions | One of the most important is that Einstein's theory incorporates the cosmic speed limit: the speed of light. Newton had assumed that gravity is felt everywhere in the Universe instantaneously, in other words that it travels at infinite speed. | The Science of Universe | Facebook
FacebookThe Science of Universe
已浏览 46.3万 次3 周前
热门视频
SOLVED: Prove that a vector space is infinite-dimensional if and only if it contains an infinite linearly indcpendent subset.
SOLVED: Prove that a vector space is infinite-dimensional if and only if it contains an infinite linearly indcpendent subset.
numerade.com
2021年12月21日
Prove that R^∞ is an infinite-dimensional vector space. | Numerade
Prove that R^∞ is an infinite-dimensional vector space. | Numerade
numerade.com
2021年9月24日
Prove that if V is an infinite-dimensional Hilbert space, then the Banach space ℬ(V, V) is nonseparable. | Numerade
Prove that if V is an infinite-dimensional Hilbert space, then the Banach space ℬ(V, V) is nonseparable. | Numerade
numerade.com
2021年7月5日
Multiverse Explained
Multiverse Theory Explained: Does the Multiverse Really Exist? Truth of Multiple Realities
6:32
Multiverse Theory Explained: Does the Multiverse Really Exist? Truth of Multiple Realities
YouTubeScience ABC
已浏览 5.1万 次2021年10月26日
What is Multiverse: The Multiverse Explained | Info Family
10:15
What is Multiverse: The Multiverse Explained | Info Family
YouTubeInfo Family
已浏览 23万 次2023年11月27日
PROOF of MULTIVERSE FOUND! | New EXPERIMENT Proves Existence Of Multiverse
15:05
PROOF of MULTIVERSE FOUND! | New EXPERIMENT Proves Existence Of Multiverse
YouTubeGetsetflySCIENCE by Gaurav
已浏览 237.9万 次2023年11月10日
SOLVED: Prove that a vector space is infinite-dimensional if and only if it contains an infinite linearly indcpendent subset.
SOLVED: Prove that a vector space is infinite-dimensional if and only i…
2021年12月21日
numerade.com
Prove that R^∞ is an infinite-dimensional vector space. | Numerade
Prove that R^∞ is an infinite-dimensional vector space. | Nume…
2021年9月24日
numerade.com
Prove that if V is an infinite-dimensional Hilbert space, then the Banach space ℬ(V, V) is nonseparable. | Numerade
Prove that if V is an infinite-dimensional Hilbert space, then th…
2021年7月5日
numerade.com
Explain why the space ℙ of all polynomials is an infinite-dimensional space. | Numerade
Explain why the space ℙ of all polynomials is an infinite-dimensi…
2021年1月13日
numerade.com
Let X be an infinite-dimensional Banach space. Show that SX​ is... | Filo
Let X be an infinite-dimensional Banach space. Show that SX​ is... | …
已浏览 5462 次5 个月之前
askfilo.com
Why space has exactly three dimensions
Why space has exactly three dimensions
2015年7月17日
newscientist.com
Physicist Explains Dimensions in 5 Levels of Difficulty | WIRED
28:24
Physicist Explains Dimensions in 5 Levels of Difficulty | WIRED
已浏览 973.4万 次2019年10月16日
YouTubeWIRED
30:20
Lec - 25 Riesz's Lemma || Proof || Concept
已浏览 4.4万 次2020年10月7日
YouTubeMy Dear Maths
49:02
ME565 Lecture 13: Infinite Dimensional Function Spaces an…
已浏览 1.5万 次2016年4月27日
YouTubeSteve Brunton
18:03
Particle in 3-dimensional box
已浏览 3.5万 次2023年1月16日
YouTubeChemWis
33:22
Infinitesimal displacement, area and volume in spherical polar coordin…
已浏览 3715 次2020年10月3日
YouTubeSpectrum
25:01
Is the Universe Infinite? - 4k
已浏览 51.2万 次2019年10月28日
YouTubeSpaceRip
Example of Infinite Dimensional Spaces in Linear Algebra and Geo…
已浏览 1848 次2018年8月19日
YouTubeIllicit Knowledge
5:32
A Basis for the Vector Space of Polynomials of Degree at Most 2
已浏览 1.4万 次2021年3月7日
YouTubeDrG DVC Math
16:23
Vector Spaces 2: Proof that R over Q is of infinite dimension
已浏览 1.7万 次2016年1月12日
YouTubemathAHA
vector space | finite,infinite dimensional space | linear algebr…
已浏览 2505 次2021年6月30日
YouTubeMathematics Skills Academy
10:02
The Multiverse Hypothesis Explained by Neil deGrasse Tyson
已浏览 608.4万 次2020年11月28日
YouTubeScience Time
11:14
[Linear Algebra] Dimension
已浏览 6.2万 次2016年5月23日
YouTubeTrevTutor
13:20
Independence, Basis, and Dimension
已浏览 44.6万 次2016年5月6日
YouTubeMIT OpenCourseWare
6:33
THE 4TH & 5TH DIMENSION EXPLAINED!
已浏览 6.7万 次2020年7月28日
YouTubeDaniel Grogan - Celestial Consciousness
16:39
Is The Universe Finite?
已浏览 168.8万 次2019年12月2日
YouTubePBS Space Time
1:03
What is infinity?
已浏览 2.4万 次2014年2月7日
YouTubeWorld Science U
1:55
How to Count Infinity
已浏览 222.1万 次2012年5月12日
YouTubeminutephysics
8:57
The Scale Beyond The Universe
已浏览 135.9万 次2019年4月18日
YouTubeDodeca
31:20
Lecture 04 : Vector Subspace: Examples and Properties
已浏览 3.4万 次2021年7月10日
YouTubeIIT Roorkee July 2018
19:52
Finite Dimensional Vector Spaces Part 1
已浏览 1.9万 次2015年7月19日
YouTubeElliot Nicholson
1:42
Infinite Space - Nintendo DS trailer
已浏览 2.5万 次2010年1月13日
YouTubeSEGA Europe
12:23
Can Space Be Infinitely Divided?
已浏览 81.5万 次2021年6月16日
YouTubePBS Space Time
30:18
How Big Is The Universe?
已浏览 313.3万 次2021年6月10日
YouTubeCool Worlds
观看更多视频
静态缩略图占位符