Interpreting linear model formula in limma package

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Here is my code for building a design matrix for a linear modelling function:

f <- factor(targets$Sample.Name, levels = unique(targets$Sample.Name))
design <- model.matrix(~0 + f)
colnames(design) <- levels(f)

Am not sure how to interpret the formula "~0". I looked up ?lm() and found that if a formula has an implied intercept term one can remove this using either y ~ x - 1 or y ~ 0 + x, but am not sure if this is the same case here.

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Yes it's the same case here. You can examine the output from design to check.