# diag

Create diagonal matrix or get diagonal elements of matrix

## Description

example

D = diag(v) returns a square diagonal matrix with the elements of vector v on the main diagonal.

example

D = diag(v,k) places the elements of vector v on the kth diagonal. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

example

x = diag(A) returns a column vector of the main diagonal elements of A.

example

x = diag(A,k) returns a column vector of the elements on the kth diagonal of A.

## Examples

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Create a 1-by-5 vector.

v = [2 1 -1 -2 -5];

Use diag to create a matrix with the elements of v on the main diagonal.

D = diag(v)
D = 5×5

2     0     0     0     0
0     1     0     0     0
0     0    -1     0     0
0     0     0    -2     0
0     0     0     0    -5

Create a matrix with the elements of v on the first super diagonal (k=1).

D1 = diag(v,1)
D1 = 6×6

0     2     0     0     0     0
0     0     1     0     0     0
0     0     0    -1     0     0
0     0     0     0    -2     0
0     0     0     0     0    -5
0     0     0     0     0     0

The result is a 6-by-6 matrix. When you specify a vector of length n as an input, diag returns a square matrix of size n+abs(k).

Get the elements on the main diagonal of a random 6-by-6 matrix.

A = randi(10,6)
A = 6×6

9     3    10     8     7     8
10     6     5    10     8     1
2    10     9     7     8     3
10    10     2     1     4     1
7     2     5     9     7     1
1    10    10    10     2     9

x = diag(A)
x = 6×1

9
6
9
1
7
9

Get the elements on the first subdiagonal (k=-1) of A. The result has one fewer element than the main diagonal.

x1 = diag(A,-1)
x1 = 5×1

10
10
2
9
2

Calling diag twice returns a diagonal matrix composed of the diagonal elements of the original matrix.

A1 = diag(diag(A))
A1 = 6×6

9     0     0     0     0     0
0     6     0     0     0     0
0     0     9     0     0     0
0     0     0     1     0     0
0     0     0     0     7     0
0     0     0     0     0     9

## Input Arguments

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Diagonal elements, specified as a vector. If v is a vector with N elements, then diag(v,k) is a square matrix of order N+abs(k).

diag([]) returns an empty matrix, [].

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Input matrix. diag returns an error if ndims(A) > 2.

diag([]) returns an empty matrix, [].

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Diagonal number, specified as an integer. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

For an m-by-n matrix, k is in the range $\left(-m+1\right)\le k\le \left(n-1\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}.$

## Tips

• The trace of a matrix is equal to sum(diag(A)).