Probability theory | Algebra of random variables | Randomness
In probability theory and statistics, a complex random vector is typically a tuple of complex-valued random variables, and generally is a random variable taking values in a vector space over the field of complex numbers. If are complex-valued random variables, then the n-tuple is a complex random vector. Complex random variables can always be considered as pairs of real random vectors: their real and imaginary parts. Some concepts of real random vectors have a straightforward generalization to complex random vectors. For example, the definition of the of a complex random vector. Other concepts are unique to complex random vectors. Applications of complex random vectors are found in digital signal processing. (Wikipedia).
Vectors (2 of 4: Representing addition & subtraction of complex numbers with vectors)
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From playlist Complex Numbers
Complex Numbers as Vectors (2 of 3: Subtraction)
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From playlist Complex Numbers
Complex Matrices ( An intuitive visualization )
Complex Matrices are not given enough credit for what they do and even when they are used its often introduced as an foreign entity. This video was made to shed light on such a misinterpreted topic. Timestamps 00:00 - Introduction 00:11 - Matrix 00:45 - Complex Number 02:50 - Complex Ma
From playlist Summer of Math Exposition Youtube Videos
Vectors (1 of 4: Outline of vectors and their ability to represent complex number)
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From playlist Complex Numbers
Given a vector find the unit vector u and check your answer
Learn how to determine the unit vector of a vector in the same direction. The unit vector is a vector that has a magnitude of 1. The unit vector is obtained by dividing the given vector by its magnitude. #trigonometry#vectors #vectors
From playlist Vectors
This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle. http://mathispower4u.yolasite.com/
From playlist Vectors
What is the formula for a unit vector from a vector in component form
http://www.freemathvideos.com In this video series I will show you how to find the unit vector when given a vector in component form and as a linear combination. A unit vector is simply a vector with the same direction but with a magnitude of 1 and an initial point at the origin. It is i
From playlist Vectors
In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im
From playlist Complex Numbers
Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)
Lecture 1 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded January 14, 2008 at Stanford University. This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of mode
From playlist Course | Modern Physics: Quantum Mechanics
Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)
Lecture 1 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded January 14, 2008 at Stanford University. This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of mode
From playlist Quantum Mechanics Prof. Susskind & Feynman
Recent progress in query complexity I & II - Pei Wu
Computer Science/Discrete Mathematics Seminar II Topic: Recent progress in query complexity I & II Speaker: Pei Wu Affiliation: Member, School of Mathematics Date: October 5, 2021 The query model is one of the most basic computational models. In contrast to the Turing machine model, fu
From playlist Mathematics
Non-Hermitian gauge field, non-Hermitian flow and quantum localization by Naomichi Hatano
PROGRAM NON-HERMITIAN PHYSICS - PHHQP XVIII DATE :04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Qua
From playlist Non-Hermitian Physics - PHHQP XVIII
Lec 19 | MIT 6.450 Principles of Digital Communications I, Fall 2006
Lecture 19: Baseband detection and complex Gaussian processes View the complete course at: http://ocw.mit.edu/6-450F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006
John Terilla : A collection of Homotopy Random Variables
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Finding the Unit Vector of a Vector in Standard Form
Learn how to determine the unit vector of a vector in the same direction. The unit vector is a vector that has a magnitude of 1. The unit vector is obtained by dividing the given vector by its magnitude. #trigonometry#vectors #vectors
From playlist Vectors
Solving Laplacian Systems of Directed Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Solving Laplacian Systems of Directed Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: March 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Recovery of ridge functions in the uniform norm – Sebastian Mayer, Universität Bonn
Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can
From playlist Approximating high dimensional functions
Michael Farber: Topology of large random spaces
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology I will discuss various models producing large random spaces (simplicial complexes and closed manifolds). The main goal is to analyse properties which hold with proba
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
Today, we take a look at how we can represent complex numbers in matrix form.
From playlist Complex Analysis
Ankur Moitra: "Tensor Decompositions and their Applications (Part 2/2)"
Watch part 1/2 here: https://youtu.be/UyO4igyyYQA Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensor Decompositions and their Applications (Part 2/2)" Ankur Moitra - Massachusetts Institute of Technology Abstract: Tensor decompositions play
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021