A scalar is an element of a field which is used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector.In linear algebra, real numbers (or other elements of a field) are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a scalar to produce another vector. More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. Then the scalars of that vector space will be the elements of the associated field.
A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar. A vector space equipped with a scalar product is called an inner product space.
The real component of a quaternion is also called its scalar part.
The term is also sometimes used informally to mean a vector, matrix, tensor, or other, usually, "compound" value that is actually reduced to a single component. Thus, for example, the product of a 1 × n matrix and an n × 1 matrix, which is formally a 1 × 1 matrix, is often said to be a scalar.
The term scalar matrix is used to denote a matrix of the form kI where k is a scalar and I is the identity matrix.
Homework Statement
Vectors
u=(-2, 9, 6)
v=(-3, 2, 1)
w=(1, 7, 5)
Homework Equations
Show that there is no scalar (Cn) such that:
C1(u) + C2(v) + C3(w) = (0, 5, 4)
I'd also like to know where would I start to find all the scalars if there were any, since I'm pretty sure this...
At page 52 of 4th chapter in "An Introduction to gauge theories & modern particle physics" by Leader & Predazzi one can find such statement:
"We must therefore rearrange (4.2.4) so that we can identify the field that multiplies\frac{1}{2}\left(1+\tau_{3}\right) as gauge boson that remains...
i know that a scalar quantity is something with magnitude and a vector is something with magnitude and direction but how do u apply that in maths. what's the difference between scalar multiplication and vector multiplication...?
if its not too hard could u dumb it down. am not all that smart...
Homework Statement
If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?
Homework Equations
Know how to do the cross product and dot product
The Attempt at a Solution
For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an...
Are there any differences between a Lorentz scalar quantity or a Lorentz invariant quantity?
That sound be stupid but we dindt find anything exaustive about that.
Take as example the power irradiate by an accelerated charge (Larmor formula, relativistic one). The expression for evaluating in...
This came up in a newsgroup but there was only one person responding who would only repeat himself regardless of what was posted. I'm looking for more insight into how people read this regarding scalars.
In Geoetricaal methods of mathematical physics by Bernard F. Schutz the author defines...
help the newbi please
I had a question about vectors and scalars. Can you explain it to me, and I also had a problem with this question.
here is the question:
Three vectors A,B, and c having magnitude of 50 units like in the x-y plane and makes angle of 30, 195,315 with positve x axis. find...
ok...
Is it possible to use the formula to decide whther a physical quantity is a scalar or a vector?
eg:
Velocity=change in displacement/time
Thus, since displacement is a vector,
therefore, velocity is also a vector>?
And for density...
Density=mass/volume
SInce mass and...
Hello, just hoping someone can give me a hand here.
I have a second-order tensor P, which has components p_{ij} and I want to show that the following scalar quantities are unchanged by rotation:
p_{ii}
p_{ij}p_{ji}
p_{ij}p_{jk}p_{ki}
Now, I know scalars are zero'th order tensors, I...
vector U is an unkown vector; known vectors are vectorA and vectorB and scalarF. vectorA (cross) vectorU = vectorB and vectorA (dot) vectorU = F. Express vectorU in terms of vectorA, vectorB, scalarF and the magnitude of vectorA.
Thank you
I saw this question posted yesterday, and now got a similar question to work out.
A = (6i-8j) cm
B = (-8i+3j) cm
C = (26i+19j) cm
aA+bB+C=0
Determine the two scalars a and b.
Ideas anyone??
Thanks
Dora
A=6i-8j m, B= -8i=3j m
I know how to add and multiply vectors, but how do I find the two scalars of a and b?
Also, I can’t figure out how to find the unit vector and direction of Resultant Vectors.
Please Help!
Thanks
Amil
A=6i-8j m, B= -8i=3j m
I know how to add and multiply vectors, but how do I find the two scalars of a and b?
Also, I can’t figure out how to find the unit vector and direction of Resultant Vectors.
Please Help!
Thanks
Amil
What is the difference between a scalar field and a vector field?
If I had a point mass with vectors pointing in all directions from its surface
the field of the mass could be said to have a magnitude and direction in all directions.I could call this a scalar because it is different from a...
The STO (Stellated Truncated Octahedron)
Peep this---->
http://groups.msn.com/shamanism/shoebox.msnw?action=ShowPhoto&PhotoID=7
I first came across this polyhedron geometric shape reading Allan Holden's Space, Shapes, and Symmetry. No refference or information is alluded to in the...
When we discuss vector properties in one dimension, most texts will drop the i, j and k notation and use instead positive and negative signs to denote direction. A scalar value to me is an absolute value. It should have no sign whatsoever. No one can ever have a "negative" speed because that...