Linear algebra | Geometric algebra | Clifford algebras | Scalars
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not. Any scalar product between a pseudovector and an ordinary vector is a pseudoscalar. The prototypical example of a pseudoscalar is the scalar triple product, which can be written as the scalar product between one of the vectors in the triple product and the cross product between the two other vectors, where the latter is a pseudovector. A pseudoscalar, when multiplied by an ordinary vector, becomes a pseudovector (axial vector); a similar construction creates the pseudotensor. Mathematically, a pseudoscalar is an element of the top exterior power of a vector space, or the top power of a Clifford algebra; see pseudoscalar (Clifford algebra). More generally, it is an element of the canonical bundle of a differentiable manifold. (Wikipedia).
QED Prerequisites Geometric Algebra 18: Complex Conjugation (Corrected)
In this lesson we cover the concept of complex conjugation of complex scalars and complex vectors. This version of this lesson has been repaired. The previous version was incorrectly edited. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The softwar
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 14: The Pseudoscalar
In this lesson we introduce the basis element of the grade 4 part of the spacetime algebra: the pseudoscalar. ERRATA: At about 6:00 I do a demonstration and slipped into the (-1,1,1,1) metric convention for a moment when I said (gamma_0)^2 = -1 …. An easy mistake to make! The result is st
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 15: Complex Structure
In this lesson we introduce the idea of "complex structure". Complex structure binds scalars with pseudoscalars, vectors with pseudovectors, and bivectors with other bivectors. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually u
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 17 - Bivector products
We examine Bivector-Bivector products using the canonical bivector form. Then we do a bit of bivector-bivector multiplication practice in the second half of the lesson, with a focus on the signature of the resulting product. Please consider supporting this channel on Patreon: https://www
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 24 Paravectors
In this lesson we discover yet another way to partition the components of a general multivector. In this method, the partitioning is entirely dependent on a choice of reference frame. That is \gamma_0 must be chosen and it represents the 4-velocity of an observer who is stationary in that
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 16: Canonical Bivectors
In this lesson we handle a few errata and then decompose a general bivector into a canonical form. Take note: we study this decomposition using a *different* paper, one written by Hestenes, but this is just a small diversion from our main paper. Please consider supporting this channel o
From playlist QED- Prerequisite Topics
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra
Geometric Algebra - Linear Transformations, Outermorphism, and the Determinant
In this video, we will review some basic concepts from linear algebra, such as the linear transformation, prove important theorems which ground matrix operations, extend the linear transformation on vectors to higher-graded elements to bivectors and trivectors, and define the determinant o
From playlist Geometric Algebra
Experimental Searches for low/high Mass Higgs Bosons by Arnab Purohit
DISCUSSION MEETING HUNTING SUSY @ HL-LHC (ONLINE) ORGANIZERS Satyaki Bhattacharya (SINP, India), Rohini Godbole (IISc, India), Kajari Majumdar (TIFR, India), Prolay Mal (NISER-Bhubaneswar, India), Seema Sharma (IISER-Pune, India), Ritesh K. Singh (IISER-Kolkata, India) and Sanjay Kumar S
From playlist HUNTING SUSY @ HL-LHC (ONLINE) 2021
Modeling a 2-Piece Candle Holder in GeoGebra Augmented Reality
Math Teachers: Students can use GeoGebra Augmented Reality to create surfaces formed by rotating the graph of a function y = f(x) about the x-axis! Here's how: https://www.geogebra.org/m/RKYFdQJy#material/kPNmmHgj.
From playlist GeoGebra Augmented Reality (older iOS app)
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From playlist Science Unplugged: General Relativity
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist Photoshop
New Searches for Dark Matter and Dark Sectors I - Rouven Essig
Prospects in Theoretical Physics Particle Physics at the LHC and Beyond Topic: New Searches for Dark Matter and Dark Sectors I Speaker: Rouven Essig Date: July 25th, 2017
From playlist PiTP 2017