Dot Product
... arrow over vector variables. A B C • If A is a vector, we use A (without arrow) to denote the magnitude. • Sometimes boldface is used for vector and normal font for magnitude. Thus vector=A; magnitude=A • More formally, we can indicate magnitude of a vector by vertical bars. • Thus A=|A|. Phy 221 20 ...
... arrow over vector variables. A B C • If A is a vector, we use A (without arrow) to denote the magnitude. • Sometimes boldface is used for vector and normal font for magnitude. Thus vector=A; magnitude=A • More formally, we can indicate magnitude of a vector by vertical bars. • Thus A=|A|. Phy 221 20 ...
Matrix Analysis
... columns, and usually enclosed in brackets. A matrix is real-valued (or, simply, real) if all its elements are real numbers or real-valued functions; it is complex-valued if at least one element is a complex number or a complex-valued function. If all its elements are numbers, then a matrix is called ...
... columns, and usually enclosed in brackets. A matrix is real-valued (or, simply, real) if all its elements are real numbers or real-valued functions; it is complex-valued if at least one element is a complex number or a complex-valued function. If all its elements are numbers, then a matrix is called ...
Problem Set 2
... to overflow (e.g., in the case a, b ≈ 10180 ), underflow (e.g., in the case a, b ≈ 10−180 ), and severe cancellation (e.g., in the case |a| |b|). Write (on paper) a matlab program to evaluate F that should be more robust against overflow, underflow and cancellation than the direct implementation. It i ...
... to overflow (e.g., in the case a, b ≈ 10180 ), underflow (e.g., in the case a, b ≈ 10−180 ), and severe cancellation (e.g., in the case |a| |b|). Write (on paper) a matlab program to evaluate F that should be more robust against overflow, underflow and cancellation than the direct implementation. It i ...
PDF
... vector space V with the usual pointwise addition and scalar multiplication of functions. In particular, the set of functions with zero Lp -norm form a linear subspace of V , which for this article will be called K. We are then interested in the quotient space V /K, which consists of complex function ...
... vector space V with the usual pointwise addition and scalar multiplication of functions. In particular, the set of functions with zero Lp -norm form a linear subspace of V , which for this article will be called K. We are then interested in the quotient space V /K, which consists of complex function ...
Lines and planes
... where θ denotes the angle between ~v and w. ~ The interested reader is advised to do this by using the law of cosines from trigonometry (see Exercise 4 and 5). In particular, we see that ~v · w ~ = 0 if and only if ~v and w ~ meet at a right angle. Motivated by this we say (in any dimension) that tw ...
... where θ denotes the angle between ~v and w. ~ The interested reader is advised to do this by using the law of cosines from trigonometry (see Exercise 4 and 5). In particular, we see that ~v · w ~ = 0 if and only if ~v and w ~ meet at a right angle. Motivated by this we say (in any dimension) that tw ...
PHYS-2100 Introduction to Methods of Theoretical Physics Fall 1998 1) 2)
... b) Explain why both E L and E R solve the wave equation in free space. π π 3π π c) Plot the vectors E L and E R for z = 0 and for t = 0, -------, -------, -------, ----, … . Explain why 4ω 2ω 4ω ω these are called “left” and “right”-handed circularly polarized waves. 3) This problem desribes a simpl ...
... b) Explain why both E L and E R solve the wave equation in free space. π π 3π π c) Plot the vectors E L and E R for z = 0 and for t = 0, -------, -------, -------, ----, … . Explain why 4ω 2ω 4ω ω these are called “left” and “right”-handed circularly polarized waves. 3) This problem desribes a simpl ...
