Homework Help: math

Posted by kevin on Tuesday, January 11, 2011 at 5:54am.

A matrix A is said to be skew symmetric if A^T = -A. Show that is a matrix is skew symmetric then its diagonal entries must all be 0.

A^T meant to be A transpose.

math - MathMate, Tuesday, January 11, 2011 at 7:31pm
Let a(i,j) stand for the element of A on the ith row and jth column.

Let
A be a skew symmetric matrix.

By the definition of skew-symmetry,
a(j,i)=-a(i,j)

On the diagonal,
i=j
=> a(i,i)=-a(i,i)
=> a(i,i)=0

since x=-x => x=0

Answer this Question

Related Questions

linear algebra - 3. Suppose A is symmetric positive definite and Q is an ...
MATHS----Matrix - For a given square matrix A the predicted values of matrix B ...
math - in a skew symmetric, how do we explain that its diagonal entries has to ...
Math - Mark each of the following True or False. ___ a. All vectors in an ...
algebra - Hi guys: Can any one please tell me what does this means? Thanks...
Discrete Math - a) Show that the relation R on Z x Z defined by (a , b) R (c, d...
Statistics - What kind of transformation will remove a right skew or a left skew...
Diagonalize - construct a nondiagonal 2 x 2 matrix that is diagonalizable but ...
Math - Is the following function symmetric with respect to the y-axis, symmetric...
math - Hi, I just want to make sure I am doing this right: Construct a relation ...

For Further Reading

First Name:
School Subject:
Answer: