- #1
xiaobai5883
- 22
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Homework Statement
1) Explain why the set W={(x,y)inside dimension 2; |x|=|y|} is not a real subspace
2) Show that the set V={[a b];a+d=0} is a real subspace of dimension 3
{[c d] }
a = -d
b = b
c = c
d = d
Take another look at post 7. I fixed the bad LaTeX tags I had earlier, so you'll be able to see what I had in there that wasn't showing.xiaobai5883 said:wait wait...
hold on...
still another question...
how about the finding of the basis for V??
is it i need to let 3 matrix myself and find the basis by that??
A real subspace is a subset of a vector space that contains all linear combinations of its vectors and is closed under scalar multiplication. It can also be defined as a subspace that only contains real numbers as its scalars.
A real subspace only contains real numbers as its scalars, while a non-real subspace can contain complex numbers as its scalars.
Yes, a complex vector space can be considered a real subspace if all of its vectors have real components and only real numbers are used as scalars.
Examples of real subspaces include the set of all real-valued polynomials, the set of all real-valued functions, and the set of all real-valued matrices.
Real subspaces are used in various fields of science and engineering, such as physics, computer science, and economics, to model and solve real-world problems. They are also used in linear algebra and functional analysis to study vector spaces and their properties.