Question

Using the compact storage technique described in Section 6.8, determine the vectors DIAG, OFFDIAG, COL, and ROW for the following matrix:

$\left[\begin{array}{cccccc}\mathbf{17}& \mathbf{-}\mathbf{9}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{-}\mathbf{2}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{7}\mathbf{.}\mathbf{1}\\ \mathbf{-}\mathbf{9}\mathbf{.}\mathbf{1}& \mathbf{25}& \mathbf{-}\mathbf{8}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{1}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{6}\mathbf{.}\mathbf{1}& \mathbf{0}\\ \mathbf{0}& \mathbf{-}\mathbf{8}\mathbf{.}\mathbf{1}& \mathbf{9}& \mathbf{0}& \mathbf{0}& \mathbf{0}\\ \mathbf{0}& \mathbf{-}\mathbf{1}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{2}& \mathbf{0}& \mathbf{0}\\ \mathbf{-}\mathbf{2}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{6}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{14}& \mathbf{-}\mathbf{5}\mathbf{.}\mathbf{1}\\ \mathbf{-}\mathbf{7}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{0}& \mathbf{-}\mathbf{5}\mathbf{.}\mathbf{1}& \mathbf{15}\end{array}\right]$

Short answer

Therefore, the vectors DIAG, OFFDIAG, COL and ROW are

$$\begin{gathered} \left[1725921415\right], \\ \left[-9.1-2.1-7.1-9.1-8.1-1.1-6.1-8.1-1.1-2.1-6.1-5.1-7.1-5.1\right], \\ [25613452212615]\mathrm{and}\left[341132\right]. \end{gathered}$$

Step-by-step solution

Given data.

Write the given matrix.

$A=\left[\begin{array}{cccccc}\mathbf{17}& \mathbf{-}\mathbf{9}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{-}\mathbf{2}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{7}\mathbf{.}\mathbf{1}\\ \mathbf{-}\mathbf{9}\mathbf{.}\mathbf{1}& \mathbf{25}& \mathbf{-}\mathbf{8}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{1}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{6}\mathbf{.}\mathbf{1}& \mathbf{0}\\ \mathbf{0}& \mathbf{-}\mathbf{8}\mathbf{.}\mathbf{1}& \mathbf{9}& \mathbf{0}& \mathbf{0}& \mathbf{0}\\ \mathbf{0}& \mathbf{-}\mathbf{1}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{2}& \mathbf{0}& \mathbf{0}\\ \mathbf{-}\mathbf{2}\mathbf{.}\mathbf{1}& \mathbf{-}\mathbf{6}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{14}& \mathbf{-}\mathbf{5}\mathbf{.}\mathbf{1}\\ \mathbf{-}\mathbf{7}\mathbf{.}\mathbf{1}& \mathbf{0}& \mathbf{0}& \mathbf{0}& \mathbf{-}\mathbf{5}\mathbf{.}\mathbf{1}& \mathbf{15}\end{array}\right]$

Here, matrix is stored in A.

Determine the definition of terms.

Write the definitions of the codes below:

The code DIAG represents the diagonal elements of the matrix.

The code OFFDIAG represents the off - diagonal elements of the matrix.

The code COL represents the position of elements of OFFDIAG in a column.

The code ROW represents number of non-zero elements in each row except diagonal elements.

Determine the vectors.

Determine the vector DIAG.

$\mathrm{DIAG}=\left[1725921415\right]$

Therefore, the diagonal elements are listed.

Determine the vector OFFDIAG.

$\mathrm{OFFDIAG}=$

$\left[-9.1-2.1-7.1-9.1-8.1-1.1-6.1-8.1-1.1-2.1-6.1-5.1-7.1-5.1\right]$

So, non-zero off-diagonal elements are listed.

Determine the vector COL.

$COL=\left[25613452212615\right]$

Here, first element representing that the, first element from OFFDIAG $-9.1$is from second column of matrix A.

Determine the vector ROW.

$ROW=\left[341132\right]$

Here, first element representing that the, first row has 3 non-zero elements except off diagonal elements.

Therefore, the vectors DIAG, OFFDIAG, COL and ROW are ,

$$\begin{gathered} \left[1725921415\right], \\ \left[-9.1-2.1-7.1-9.1-8.1-1.1-6.1-8.1-1.1-2.1-6.1-5.1-7.1-5.1\right] \\ \left[25613452212615\right]and\left[341132\right]. \end{gathered}$$