Programming

Operating on Diagonal Matrices

There are several MATLAB functions that work specifically on diagonal matrices.

Function	Description
blkdiag	Construct a block diagonal matrix from input arguments.
diag	Return a diagonal matrix or the diagonals of a matrix.
trace	Compute the sum of the elements on the main diagonal.
tril	Return the lower triangular part of a matrix.
triu	Return the upper triangular part of a matrix.

Constructing a Matrix from a Diagonal Vector

The diag function has two operations that it can perform. You can use it to generate a diagonal matrix:

• A = diag([12:4:32])
  A =
      12     0     0     0     0     0
       0    16     0     0     0     0
       0     0    20     0     0     0
       0     0     0    24     0     0
       0     0     0     0    28     0
       0     0     0     0     0    32
  

You can also use the diag function to scan an existing matrix and return the values found along one of the diagonals:

• A = magic(5)
  A =
      17    24     1     8    15
      23     5     7    14    16
       4     6    13    20    22
      10    12    19    21     3
      11    18    25     2     9
  
  diag(A, 2)       % Return contents of second diagonal of A
  ans =
       1
      14
      22
  

Sorting Row Vectors

Returning a Triangular Portion of a Matrix

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