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An index vector can be formed using several methods in different programming languages. Here are a few examples:

1. In Python, an index vector can be formed using the range function, which creates a sequence of integers from a starting point to an ending point, with a specified increment:

index_vec = list(range(start, end, increment))

For example, to create an index vector with values from 0 to 9:

index_vec = list(range(0, 10))

1. In R, an index vector can be formed using the colon operator, which generates a sequence of values from a starting point to an end point:

index_vec <- start:end

For example, to create an index vector with values from 1 to 5:

index_vec <- 1:5

1. In MATLAB, an index vector can be formed using the colon operator as well, which creates a row vector with a sequence of values from a starting point to an end point:

index_vec = start:end

For example, to create an index vector with values from 0 to 4:

index_vec = 0:4