0-based indexing

Definition: Indexing (an array) beginning with 0.

Note: That is, an array A with n items is accessed as A[0], A[1], ..., A[n-1].

one-based indexing

Definition: Indexing (an array) beginning with 1.

Note: That is, an array A with n items is accessed as A[1], A[2], ..., A[n].

lower triangular matrix

Definition: A matrix that is only defined at (i,j) when i ≥ j.

Note: For example

	j
i	1	-	-	-
	7	7	-	-
	1	0	1	-
	1	9	5	4

It may be more compactly represented in an array by storing entry (i,j) in location

i(i-1)/2 + j (one-based indexing).

upper triangular matrix

Definition: A matrix that is only defined at (i,j) when i ≤ j.

Note: For example

	j
i	1	7	7	6
	-	9	1	1
	-	-	8	8
	-	-	-	1

It may be more compactly represented in an array by storing entry (i,j) in location n(i-1) + j - i(i-1)/2 = (2n-i)(i-1)/2 + j one-based indexing.

strictly upper triangular matrix

Definition: A matrix that is only defined at (i,j) when i < j.

Note: For example

	j
i	-	7	7	6
	-	-	1	1
	-	-	-	8
	-	-	-	-

It may be more compactly represented in an array by storing entry (i,j) in location n(i-1) + j - i(i-1)/2 - i = (2n-i)(i-1)/2 - i + j (one-based indexing).

strictly lower triangular matrix

Definition: A matrix that is only defined at (i,j) when i > j.

Note: For example

	j
i	-	-	-	-
	7	-	-	-
	1	0	-	-
	1	9	5	-

It may be more compactly represented in an array by storing entry (i,j) in location (i-1)(i-2)/2 + j (one-based indexing).