Linear algebra | Geometric topology | Dimension | Algebraic geometry
In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension. In linear algebra, given a quotient map , the difference dim V − dim Q is the relative dimension; this equals the dimension of the kernel. In fiber bundles, the relative dimension of the map is the dimension of the fiber. More abstractly, the codimension of a map is the dimension of the cokernel, while the relative dimension of a map is the dimension of the kernel. These are dual in that the inclusion of a subspace of codimension k dualizes to yield a quotient map of relative dimension k, and conversely. The additivity of codimension under intersection corresponds to the additivity of relative dimension in a fiber product. Just as codimension is mostly used for injective maps, relative dimension is mostly used for surjective maps. (Wikipedia).
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
Absolute versus relative measurements in geometry | Rational Geometry Math Foundations 134
In science and ordinary life, the distinction between absolute and relative measurements is very useful. It turns out that in mathematics this is also an important distinction. We must be prepared that some aspects of mathematics are more naturally measured relatively, rather than absolute
From playlist Math Foundations
This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Johan de Jong - Affineness of the complement of the ramification locus - WAGON
The purpose of this talk is to encourage people to think about purity questions. We will discuss a strong form of purity for morphisms of relative dimension 0. For morphisms of relative dimension 1 we relate the purity question to one on purity for families of curves.
From playlist WAGON
Lec 22. Einstein's General Relativity and Gravitation: Student Presentations. Group 2
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 22. Einstein's General Relativity and Gravitation -- Student Presentation -- Group 2 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W.
From playlist Einstein's General Relativity and Gravitation
Colloquium MathAlp 2016 - Michel Ledoux
Isopérimétrie dans les espaces métriques mesurés Le problème isopérimétrique (à volume donné, minimiser la mesure de bord, et déterminer les ensembles extrémaux), remonte aux temps les plus anciens. Tout à la fois, il peut se formuler de façon générale dans un espace métrique mesuré, et d
From playlist Colloquiums MathAlp
Helvi Witek - Introduction to Numerical Relativity, Part 1 of 2 - IPAM at UCLA
Recorded 14 September 2021. Helvi Witek of the University of Illinois presents "Introduction to Numerical Relativity" at IPAM's Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy Tutorial. This is the first of two parts of Helvi's presentation. Abstract: I
From playlist Tutorials: Math & Computational Challenges in the Era of Gravitational Wave Astronomy
Projectivity of the moduli space of KSBA stable pairs and applications - Zsolt Patakfalvi
Zsolt Patakfalvi Princeton University February 24, 2015 KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli spac
From playlist Mathematics
Absolute vs. relative Gromov-Witten invariants - Tehrani
Topic: Absolute vs. relative Gromov-Witten invariants Speaker: Mohammad Tehrani Date: Friday, December 18 We compare absolute and relative Gromov-Witten invariants with the basic contact vector for very positive divisors. For such divisors, one might expect that these invariants are the s
From playlist Mathematics
Is space-time fragmented, segmented into quantized bits of information, or causal sets? Or is space-time smooth and continuous, with curves, bends, and warps; just as Einstein had predicted? Is what we call space-time even part of objective reality or is it just a mathematical construct
From playlist Science
Zhizhang Xie: A relative index theorem for incomplete manifolds and Gromov’s conjectures on PSC
Talk by Zhizhang Xie in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/a-relative-index-theorem-for-incomplete-manifolds-and-gromovs-conjectures-on-positive-scalar-curvature/ on May 7, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Lisa Randall - How is the Cosmos Constructed?
What are the basic components of the cosmos? At the deepest levels of reality—the particles, fields and forces of the smallest slices of existence—how does the world work? Click here to watch more interviews on how the cosmos is constructed http://bit.ly/2odzX9J Click here to watch more
From playlist Closer To Truth - Lisa Randall Interviews
Relativity 7b - differential geometry II
The ideas Gauss developed to described the geometry of a curved two-dimensional surface is generalized to abstract N dimensional spaces. This is the most math intensive video in the series so far. This is unavoidable as we are introducing the fundamental mathematical objects that allowed E
From playlist Relativity
What is an angle and it's parts
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships