How do you convert a vector to a diagonal matrix?

D = diag( v ) returns a square diagonal matrix with the elements of vector v on the main diagonal. D = diag( v , k ) places the elements of vector v on the k th diagonal. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

Are diagonal matrices closed under multiplication?

Then cA is a diagonal matrix and A +B is diagonal matrix so the set of diagonal matrices is closed under matrix addition and scalar multiplication.

Is a vector diagonal matrix?

Closed 10 years ago. For any column vector we can easily create a corresponding diagonal matrix, whose elements along the diagonal are the elements of the column vector. For example Mx cannot work for any matrix M, since the result will be a vector, not a diagonal matrix.

How do you convert a diagonal to a matrix?

We want to diagonalize the matrix if possible.

  1. Step 1: Find the characteristic polynomial.
  2. Step 2: Find the eigenvalues.
  3. Step 3: Find the eigenspaces.
  4. Step 4: Determine linearly independent eigenvectors.
  5. Step 5: Define the invertible matrix S.
  6. Step 6: Define the diagonal matrix D.
  7. Step 7: Finish the diagonalization.

How do you multiply diagonal matrices?

Multiplication of diagonal matrices is commutative: if A and B are diagonal, then C = AB = BA. iii. If A is diagonal, and B is a general matrix, and C = AB, then the ith row of C is aii times the ith row of B; if C = BA, then the ith column of C is aii times the ith column of B.

What is the inverse of a diagonal matrix?

The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal, as illustrated below for matrix C. where I is the identity matrix. This approach will work for any diagonal matrix, as long as none of the diagonal elements is equal to zero.

How do you convert a vector to a matrix?

To convert a vector into matrix, just need to use matrix function. We can also define the number of rows and columns, if required but if the number of values in the vector are not a multiple of the number of rows or columns then R will throw an error as it is not possible to create a matrix for that vector.