1 votes 1 votes How many different entries can a 4 * 4 skew-symmetric matrix have? An n* n skew-symmetric matrix? What if it is symmetric matrix ? Mathematical Logic engineering-mathematics linear-algebra + – set2018 asked Jul 29, 2017 set2018 1.7k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply set2018 commented Jul 30, 2017 reply Follow Share @Bikram sir 0 votes 0 votes Bikram commented Jul 30, 2017 reply Follow Share @set2018 Symmetric matrices : A square matrix A = [aij] is said to be symmetric if A′ = A, that is, [aij] = [aji] for all possible values of i and j. For example is a symmetric matrix as A′ = A in this matrix, A[1,2] =2 and A[2,1]=2 .... A[1,3]=3 and A[3,1] = 3 that means [aij] = [aji] for all possible values of i and j . Skew symmetric matrices : A square matrix A = [aij] is said to be skew symmetric matrix if A′ = – A, that is aji = – aij for all possible values of i and j. Now, if we put i = j, we have aii = – aii. Therefore 2aii = 0 or aii = 0 for all i’s. This means that all the diagonal elements of a skew symmetric matrix are zero. For example, the matrix is a skew symmetric matrix as B′= –B see here A[1,2]=e but A[2,1]= -e 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes a four by four ( 4 * 4) skew-symmetric matrix is: A = 0 -a -b -c a 0 -d -e b d 0 -f c e f 0 Therefore 6 entries can be chosen independently Bikram answered Jul 30, 2017 Bikram comment Share Follow See 1 comment See all 1 1 comment reply Bikram commented Jul 30, 2017 reply Follow Share The most general form of a four by four symmetric matrix is: A = a e f g e b h i f h c j g i h d Therefore 10 entries can be chosen independently. 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes In skew symmetric matrix all diagonal elements are zero and Aij = -Aji which means only 2 entries must be different. 0 -2 2 -2 2 0 -2 2 -2 2 0 -2 2 -2 2 0 Optimus Prime answered Jul 30, 2017 Optimus Prime comment Share Follow See 1 comment See all 1 1 comment reply Tesla! commented Jul 30, 2017 reply Follow Share So if diagonal are all zero then still 12 element are there so how 2 entries can be zero? 1 votes 1 votes Please log in or register to add a comment.