# What is the dimension of the vector space of 2 by 2 matrices?

## What is the dimension of the vector space of 2 by 2 matrices?

The vector space of 2×2 matrices under addition over a field F is 4 dimensional.

## What is the dimension of the vector space of 2X2 symmetric matrices?

The space of 2 2 diagonal matrices has dimension 2.

Can a 2X2 matrix be a vector space?

According to the definition, the each element in a vector spaces is a vector. So, 2×2 matrix cannot be element in a vector space since it is not even a vector.

What is the dimension of 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.

### What is the dimension of MXN matrix?

A matrix with m rows and n columns is called an m × n matrix, or m-by-n matrix, while m and n are called its dimensions. For example, the matrix A above is a 3 × 2 matrix. Matrices with a single row are called row vectors, and those with a single column are called column vectors.

### What is the basis of symmetric matrix?

A matrix is symmetric if and only if it is equal to its transpose. All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal. A matrix is skew-symmetric if and only if it is the opposite of its transpose. All main diagonal entries of a skew-symmetric matrix are zero.

Is matrix vector space?

So, the set of all matrices of a fixed size forms a vector space. That entitles us to call a matrix a vector, since a matrix is an element of a vector space.

Is the set a vector space?

The set C(D,R) of all continuous real-valued functions defined over a given subset D of the real numbers is a real vector space: if x ↦→ f(x) and x ↦→ g(x) are continuous functions on D then so are x ↦→ f(x) + g(x) and x ↦→ cf(x) for all real numbers c; moreover these operations of addition of functions and of …