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Gene Expression Quantification

Methods for measuring the level of gene expression, such as RNA sequencing (RNA-Seq) or microarrays, often expressed as transcripts per million (TPM) or reads per kilobase per million mapped reads (RPKM).
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The statement of the theorem

Let C\mathbf{C} be the raw count matrix, where Cg,sC_{g, s} is the raw read count for gene gg in sample ss. To normalize for sequencing depth and gene length, the Transcripts Per Million (TPM) value for gene gg in sample ss, denoted Tg,sT_{g, s}, is calculated as: Tg,s=Cg,s/Lg∑k(Ck,s/Lk)×106T_{g, s} = \frac{C_{g, s} / L_g}{\sum_{k} (C_{k, s} / L_k)} \times 10^6 \nwhere LgL_g is the length of gene gg in base pairs, and the denominator ∑k(Ck,s/Lk)\sum_{k} (C_{k, s} / L_k) represents the total normalized count for sample ss.
Source: Wikipedia