Dimension of a vector space and its subspaces • Physics Forums
Jan 24, 2024 · My thought was that was a vector space and a subspace with an uncountably infinite index. I then confused index and dimension instead of building a correct counterexample.
Upper trianglar matrix is a subspace of mxn matrices
Oct 9, 2016 · Homework Statement Prove that the upper triangular matrices form a subspace of M m × n over a field F Homework Equations The Attempt at a Solution We can prove this …
Lagrangian subspaces of symplectic vector spaces - Physics Forums
Jun 4, 2012 · Homework Statement If (V,\\omega) is a symplectic vector space and Y is a linear subspace with \\dim Y = \\frac12 \\dim V show that Y is Lagrangian; that is, show that Y = …
Showing that U = { (x, y) | xy ≥ 0} is not a subspace of R^2
Nov 22, 2012 · but is that sufficient to show that U is not a subset of R 2x2? Well, first, you are not trying to show U is not a subset. It is. But it is not a subspace. I suspect that was a typo. Yes, …
Subspaces of R2 and R3: Understanding Dimensions of Real …
Mar 4, 2008 · So I'm considering dimensions of real vector spaces. I found myself thinking about the following: So for the vector space R2 there are the following possible subspaces: 1. {0} 2. …
Is there a symbol for indicating one vector space is a subspace of ...
Apr 27, 2011 · There is no universally accepted symbol to indicate that one vector space is a subspace of another. While V ⊆ W is commonly used in set notation, some prefer the notation …
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · I have a question that states: Let a, b, and c be scalers such that abc is not equal to 0. Prove that the plane ax + by + cz = 0 is a subspace of R^3.
Proving S is a Subspace of P2: A Scientific Approach
Aug 18, 2012 · Homework Statement Let S = { p \\in P_{2}(ℝ) | p(7) = 0 } Prove that S is a subspace of P_{2}(ℝ) (the vector space of all polynomials of degree at most 2) The Attempt at …
Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · 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 …
Distance from a vector to a subspace • Physics Forums
Nov 3, 2013 · 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,