Sets are associative and commutative over the symmetric difference operator, use this to combine like terms, then simplify. Similar technique can be used on variations of this identity to build your own identities which can be used as short cuts in other proofs containing the symmetric...
Is there a shorter way to verify this identity, as you can see I haven't even finished it. I know you can use Ven diagrams and truth tables but I wanted to avoid them inorder to use a more general formal approach. picture is attached
My question is more about the structure of the second expression used to define the set A.
I've just read something regarding free variables and bound variables. In the case of the second definition, x is a bound variable since the notation {x |...} binds the variable and y is a free...
I have a set, A = {1,4,9,16,25,36,49,...}, that I want to write a definition for using an elementhood test. I have written one defintion I'm sure is correct but I'm not sure if the other one is appropriate since there are values that satisfy the conditions in the definitions but produce values...
It's been a while since my last calc course and I'm not sure if I even encountered how to do this but is there a way to derive a function of a concave downward sloping curve given two or more points and their respective slopes? I'm obviously aware how the curve looks but I would like to know...
I think i may have some inaccuracies in the above post.
Nevertheless I've cleared up my confusion with these orthogonal eigenvectors and how they preserve all the properties of spaces. I saw how you plugged in values for x and y in order to cancel out the 4. However I did some more...
I went back in the primary book I'm using and saw that i was dealing with a homogeneous system of linear equations, because all the constant terms are zero, therefore there are many solutions. Then I read further into deriving general solutions, in this case
In terms of row vectors, we...
Let me add a disclaimer to my post:
I have not taken a linear algebra class, however the course I will be taking this fall09 semester uses a lot of linear algebra, where the main linear algebra techniques are covered in a preliminary pdf. I think I have done a good job of self learning many of...
I am somewhat confused about this property of an eigenvalue when A is a symmetric matrix, I will state it exactly as it was presented to me.
"Properties of the eigenvalue when A is symmetric.
If an eigenvalue \lambda has multiplicity k, there will be k (repeated k times),
orthogonal...
Something isn't completely accurate in the second sentence of the original post
"Assuming products are defined and the matrices involved are nonsingular of the same order"
since it doesn't matter if the matrices are nonsingular for this property to hold a more accurate statement would be...
I've been going through properties of determinants of matrices and found the following:
Assuming products are defined and the matrices involved are nonsingular of the same order
The determinant of the product of any number of matrices is equal to the determinant of each matrix; where the order...
EnumaElish,
The only point it may have is to illustrate my absentmindedness. Apologies for my carelessness, in no way did I intend disrespect towards you now and in any of our previous interaction, I mean that with all sincerity. I'm sure I would be perturbed as well if someone referred to...
I just want to clarify, for my sake, the difference in the wiki citation and my problem, correct me if I'm wrong.
"By contrast, if two cards are drawn without replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second...