yes
yes, it is both symmetric as well as skew symmetric
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
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They can be either. If they are roots of a real polynomial then purely imaginary would be symmetric and only real roots can be skew symmetric.
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
I could be wrong but I do not believe that it is possible other than for the null matrix.
A skew-symmetric function, also known as an antisymmetric function, is a function ( f ) that satisfies the property ( f(x, y) = -f(y, x) ) for all ( x ) and ( y ) in its domain. This means that swapping the inputs results in the negation of the function's value. Skew-symmetric functions are often encountered in fields like linear algebra and physics, particularly in the context of determinants and cross products. An example is the function ( f(x, y) = x - y ).
In a skew symmetric matrix of nxn we have n(n-1)/2 arbitrary elements. Number of arbitrary element is equal to the dimension. For proof, use the standard basis.Thus, the answer is 3x2/2=3 .
No, there cannot be any.
Symmetric Property of Congruence
In a symmetric binomial distribution, the probabilities of success and failure are equal, resulting in a symmetric shape of the distribution. In a skewed binomial distribution, the probabilities of success and failure are not equal, leading to an asymmetric shape where the distribution is stretched towards one side.