What is the dimension of all symmetric matrices?

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 the vector space of all nxn symmetric matrices?

So, the dimension is . It is n² . A basis of the vector-space V(R) of all (nxn) real matrices may be given as follows ; {B(i, j)} ; i, j = 1, 2, 3 …. .. n & where B(i, j) is a nxn matrix such that its (i, j) element = 1 and all other elements are 0 .

What will be the dimension of vector space containing all 2×2 symmetric matrices A?

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.

How do you find the dimensions of a matrix?

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 all 2×2 matrices?

The vector space of 2×2 matrices under addition over a field F is 4 dimensional. It’s span{(1000),(0100),(0010),(0001)}. These are clearly independent under addition.

What are dimensions in 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.

What is the dimension of vector space of \small 4 \times 4 real matrices with sum of all entries equal to zero?

An easier approach : There are in total 16 variables in 4 X 4 matrix. There are 4 rows ,4 columns satisfying the fixed sum property. So 16 variables and 8 equations, that means 8 variables are independent and 8 are not. So dimension of vector space is 8.