What is Skew symmetric: Definition and 20 Discussions
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition
In terms of the entries of the matrix, if
a
i
j
{\textstyle a_{ij}}
denotes the entry in the
i
{\textstyle i}
-th row and
j
{\textstyle j}
-th column, then the skew-symmetric condition is equivalent to
I am sure you are all familiar with the cross product in 3D space.
i cross into j gives k.
Cyclic
Negative, if reversed, etc.
I am sure you are all familiar with the definition as: norm of the first vector, norm of the second, sine of the angle, perpendicular (but direction using right hand...
Hello
Say I have a column of components
v = (x, y, z).
I can create a skew symmetric matrix:
M = [0, -z, y; z, 0; -x; -y, x, 0]
I can also go the other way and convert the skew symmetric matrix into a column of components.
Silly question now...
I have, in the past, referred to this as...
Hi,
if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric.
How does the equation appear if i only want a system to have the state z? do I get z_dot = -q*x + p*y. Or is the symmetric not valid so I...
Homework Statement
Need to prove that the derivative of a rotation matrix is a skew symmetric matrix muktiplied by that rotation matrix. Specifically applying it on the Rodrigues’ formula.Homework EquationsThe Attempt at a Solution
I have shown that the cubed of the skew symmetric matrix is...
Homework Statement
Hi there,
I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging.
Homework Equations
I have attached the determinant as an...
Any help would be much appreciated.
The problem lies in the non-Gaussian distribution of the sample. If we take the entire data set of total fish catch, the skewness statistic equals 7.463 with a std. error of skewness of 0.39. Accordingly, the Z dist. (7.463/0.39)=19.14. Overall, the...
Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...
I am a bit dense when it comes to linear algebra for some reason. I am reviewing math to prepare for a physics grad program, and I am using Mary Boas "Mathematical Methods in the Physical Sciences". She presents the idea of a skew symmetric matrix in the problem set rather than in the text. I...
I am asking for some hints to solve this excercise. Given an invertible skew symmetric matrix $A$, then show that there are invertible matrices $ R, R^T$ such that $R^T A R = \begin{pmatrix} 0 & Id \\ -Id & 0 \end{pmatrix}$, meaning that this is a block matrix that has the identity matrix in two...
I'm pretty inexperienced in proof writing. So not sure if this was valid.
If a matrix is skew symmetric then A^T = - A, that is the transpose of A is equal to negative A.
This implies that if A = a(i,j), then a(j,i) = -a(i,j). If we're referring to diagonal entries, we can say a(j,j) =...
Homework Statement
Let W be a 3x3 matrix where A^t(transpose)=-A. Find a basis for W.
Homework Equations
Find a basis for W.
The Attempt at a Solution
I have no idea how to start it.
Homework Statement
Show that if A is skew symmetric, then Ak is skew symmetric for any positive odd integer k.
Homework Equations
The Attempt at a Solution
Wow, I have no idea how to prove this. I'm guessing there's going to be induction involved. I know that the base case of k...
Hi all! I was working on some homework for the linear algebra section of my "Math Methods for Physicists" class and was studying skew symmetric matrices. There was a proof I saw on Wikipedia that proves that the determinant of a skew symmetric matrix is zero if the number of rows is an odd...
Homework Statement
Hi, I need to prove that if S is a skew-symmetric matrix with NXN dimension and B is any square real-valued matrix, therefore the product of transpose(B), S, and B is also askew symmetric matrix
Homework Equations
This is what I know so far.
1.Transpose(S) = -S...
Given the vector space consisting of all bilinear forms of a vector space V (let's call it B) it's very easy to prove that B is the direct sum of two subspaces, the subspace of symmetric and the subspace of skew symmetric bilinear forms. How would one go about determining the dimension of these...
Hi,
I am having trouble with the question above. In general, I have trouble with questions like:
What is the basis for all nxn matrices with trace 0? What is the dimension?
What is the basis of all upper triangular nxn matrices? What is the dimension?
Please help!
Let A be an nxn skew symmetric mx.(A^T=-A).
i) Show that if X is a vector in R^n then (X,AX)=0
ii) Show that 0 is the only possible eigenvalue of A
iii)Show that A^2 is symmetric
iv)Show that every eigenvalue of A^2 is nonpositive.
v)Show that if X is an eigenvector of A^2 , then so is AX...