What is the dimension of a 3×3 symmetric matrix?

The dimension of symmetric matrices is n(n+1)2 because they have one basis as the matrices {Mij}n≥i≥j≥1, having 1 at the (i,j) and (j,i) positions and 0 elsewhere. For skew symmetric matrices, the corresponding basis is {Mij}n≥i>j≥1 with 1 at the (i,j) position, −1 at the (j,i) position, and 0 elsewhere.

What is the dimension of a set of matrices?

The dimensions of a matrix are the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix. For example, the first matrix shown below is a 2×2 matrix; the second one is a 1×4 matrix; and the third one is a 3×3 matrix.

What is the dimension of the vector space of 2×2 symmetric matrices?

Yes, but note that the title says “diagonal matrices”, which aren’t the same as symmetric matrices. The space of 2 2 diagonal matrices has dimension 2. This is true.

What form does a 3 by 3 matrix have if it is symmetric as well as skew symmetric?

Originally Answered: What forms does a 3*3 matrix have if it is symmetric as well as skew symmetric? the entry in i th row and j th column is represented as a ij then the corresponding skew symmetric matrix is a ij = – a ji.

What is the determinant of symmetric matrix?

Symmetric Matrix Determinant Finding the determinant of a symmetric matrix is similar to find the determinant of the square matrix. A determinant is a real number or a scalar value associated with every square matrix. Let A be the symmetric matrix, and the determinant is denoted as “det A” or |A|.

What is a symmetric matrix example?

A square matrix that is equal to its transpose is called a symmetric matrix. For example, a square matrix A = aij is symmetric if and only if aij= aji for all values of i and j, that is, if a12 = a21, a23 = a32, etc. Note that if A is a symmetric matrix then A’ = A where A’ is a transpose matrix of A.