## How do you find a symmetric matrix in R?

Check if a Matrix is Symmetric or not in R Programming – isSymmetric() Function. isSymmetric() function in R Language is used to check if a matrix is a symmetric matrix.

## What is a symmetric matrix with 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.

**What does a symmetric matrix look like?**

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Because equal matrices have equal dimensions, only square matrices can be symmetric.

### How do you create a matrix in R?

To create a matrix in R you need to use the function called matrix(). The arguments to this matrix() are the set of elements in the vector. You have to pass how many numbers of rows and how many numbers of columns you want to have in your matrix. Note: By default, matrices are in column-wise order.

### How do you make a diagonal matrix in R?

diag() function in R Language is used to construct a diagonal matrix.

- Syntax: diag(x, nrow, ncol)
- Parameters:
- x: value present as the diagonal elements.
- nrow, ncol: number of rows and columns in which elements are represented.

**Is ABAB symmetric?**

This is the negative of the original difference matrix, so unless AB = BA (i.e., the original matrix is all 0’s), AB − BA cannot be symmetric. If A and B are symmetric (of the same size), must ABAB be symmetric? Well, But the same A and B = [ 1 2 2 4 ] doesn’t work: ABAB = [ 8 16 4 8 ] (not symmetric).

#### What is symmetric and skew-symmetric matrix with example?

A matrix is symmetric if and only if it is equal to its transpose. 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.

#### How to force a matrix to be symmetric in R?

You can force the matrix to be symmetric using forceSymmetric function in Matrix package in R: or just s <- 0.5 * (s + t(s)). I like your approach better since taking the mean is assuming each triangular side is equally correct (or wrong). While other solutions are arbitrarily picking one.

**How to know if a symmetric matrix is invertible?**

1 The symmetric matrix should be a square matrix. 2 The eigenvalue of the symmetric matrix should be a real number. 3 If the matrix is invertible, then the inverse matrix is a symmetric matrix. 4 The matrix inverse is equal to the inverse of a transpose matrix.

## What are the properties of a symmetric matrix?

Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. The eigenvalue of the symmetric matrix should be a real number. If the matrix is invertible, then the inverse matrix is a symmetric matrix.

## Is the eigenvalue of a symmetric matrix real?

The eigenvalue of the symmetric matrix should be a real number. The matrix inverse is equal to the inverse of a transpose matrix. If A and B be a symmetric matrix which is of equal size, then the summation (A+B) and subtraction(A-B) of the symmetric matrix is also a symmetric matrix.