MATLAB®

Operating on Diagonal Matrices

Diagonal Matrix Functions

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

Back to Top

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

Back to Top

Returning a Triangular Portion of a Matrix

The tril and triu functions return a triangular portion of a matrix, the former returning the piece from the lower left and the latter from the upper right. By default, the main diagonal of the matrix divides these two segments. You can use an alternate diagonal by specifying an offset from the main diagonal as a second input argument:

A = magic(6);

B = tril(A, -1)
B =
     0     0     0     0     0     0
     3     0     0     0     0     0
    31     9     0     0     0     0
     8    28    33     0     0     0
    30     5    34    12     0     0
     4    36    29    13    18     0

Back to Top

Concatenating Matrices Diagonally

You can diagonally concatenate matrices to form a composite matrix using the blkdiag function. See Creating a Block Diagonal Matrix for more information on how this works.

Back to Top

Shifting and Sorting Matrices

Empty Matrices, Scalars, and Vectors