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## Operating on Diagonal Matrices

### Diagonal Matrix Functions

### Constructing a Matrix from a Diagonal Vector

### Returning a Triangular Portion of a Matrix

### Concatenating Matrices Diagonally

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

Function | Description |
---|---|

Construct a block diagonal matrix from input arguments. | |

Return a diagonal matrix or the diagonals of a matrix. | |

Compute the sum of the elements on the main diagonal. | |

Return the lower triangular part of a matrix. | |

Return the upper triangular part of a matrix. |

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

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

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.

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