diag - Diagonal matrices and diagonals of matrix

Syntax

X = diag(v,k)
X = diag(v)
v = diag(X,k)
v = diag(X)

Description

X = diag(v,k) when v is a vector of n components, returns a square matrix X of order n+abs(k), with the elements of v on the kth diagonal. k = 0 represents the main diagonal, k > 0 above the main diagonal, and k < 0 below the main diagonal.

X = diag(v) puts v on the main diagonal, same as above with k = 0.

v = diag(X,k) for matrix X, returns a column vector v formed from the elements of the kth diagonal of X.

v = diag(X) returns the main diagonal of X, same as above with k = 0 .

Tips

diag(diag(X)) is a diagonal matrix.

sum(diag(X)) is the trace of X.

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

diag(m-by-1,k) generates a matrix of size m+abs(k)-by-m+abs(k).

diag(1-by-n,k) generates a matrix of size n+abs(k)-by-n+abs(k).

Examples

The statement

diag(-m:m)+diag(ones(2*m,1),1)+diag(ones(2*m,1),-1)

produces a tridiagonal matrix of order 2*m+1.

See Also

blkdiag | spdiags | tril | triu

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