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Why R2 is not a subspace of R3? - Physics Forums R^2 is isomorphic to the subset (a,b,0) of R^3, but it's also isomorphic to infinitely many other subspaces of R^3 (any 2 dimensional one) As such, there's no canonical embedding, and you don't usually think of R^2 as being contained in R^3 A more obvious explanation is the vector (a,b) is not the same as the vector (a,b,0) 2 components vs 3 components, so they are different objects
Subspaces in R4: Get Started Understand Now - Physics Forums I'm so lost! 1 W is the set of all vectors in R4 such that x1 + x3 = x2 + x4 Is W a subspace of R4 and Why? How do i get started here? I'm thoroughly confused on this whole idea of vector spaces and such
Solving Vector Subspace Questions: A B in V - Physics Forums Prove your answer b) Determine whether or not A ∪ B is a vector subspace of V Prove your answer My strategy for this is to find two subspaces in V and find a counter claim so that the union of A and B is not a subspace and similarly for the intersection of A and B would this be strategy be enough to answer the question? thanks so much
Prove the sum of two subspaces is also a subspace. Homework Equations is a subspace of if is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication The definition of a sum a vector subspace U and W is The Attempt at a Solution 1 Since and both contain the additive identity, contains the additive identity 3
Distance from a vector to a subspace - Physics Forums Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311 1 5 8 Ax=b in parametric vector form,
How to determine the smallest subspace? - Physics Forums The smallest subspace containing vectors in the list is How can one know how small a subspace is? initially I thought it was determined from the number of elements in the subspace, but there infinite number of elements Can also someone please give an example by giving two subspaces and show the ways to compare which one is smaller than which?
Subspace topology of Rationals on Reals - Physics Forums I am trying to visualize the subsppace topology that is generated when you take the Rationals as a subset of the Reals So if we have ℝ with the standard topology, open sets in a subspace topology induced by Q would be the intersection of every open set O in ℝ with Q Since each open set
Is singular matrix is a subspace of vector space V? - Physics Forums a)is S closed under addition? b) is S closed under scalar multiplication? Homework Equations S is a subspace of V if it is closed under addition and scalar multiplication The Attempt at a Solution I tried to use the definition of sinularity i e a matrix in not invertible But could not decide if it was closed under addition and scalar