What Is the Difference Between Mathematical and Physical Vector Spaces?

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Mathematical vector spaces are abstract structures defined by a set of vectors and scalar fields that adhere to specific axioms. In contrast, physical vector spaces refer to the actual environments, such as lines or planes, where vectors and vector fields are applied in the physical world. The key distinction lies in the abstract nature of mathematical vector spaces versus the tangible contexts of physical vector spaces. While both concepts involve vectors, mathematical vector spaces do not necessarily relate to physical phenomena, whereas physical vector spaces are inherently linked to real-world applications. Understanding this difference is crucial for applying vector concepts in various fields.
madiha_314
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pleasezz helpppp me as soon as possible

:cry: hi,
I want to ask you "What is the difference between mathematical vector space and physical vector space?"
I mean to say"how can we distinguish vector space in physics and maths"?
thanxz :rolleyes:
 
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huh? Do you have any idea what you just said?
No different. NO, NONE, ZIP, period
unless i misunderstood what you asked... your question is same as asking me what is the difference between the addition in physics and that in mathematics...
one more thing... vector space in mathematics is not nessissory related to our physical world... but physics will not do things that has nothing to do with our physical world... that might be the only different...
 
madiha_314 said:
:cry: hi,
I want to ask you "What is the difference between mathematical vector space and physical vector space?"
I mean to say"how can we distinguish vector space in physics and maths"?
thanxz :rolleyes:


A "mathematical vector space"(aka linear space) is an abstract set A (of elements called vectors) over a field of scalars (R,C,quaternions) whose elements satisfy the axioms of vector space...

A "physical vector space" is is the "ambient environment" for vectors and vector fields...A straight line,the plane,the 3D space are "environments" in which vectors 'defined physically' exist...

Daniel.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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