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Due to IFFT being a linear transformation, the representation of the block in the time domain is given by x = I F F T ∑ m = 1 M X m = ∑ m = 1 M I F F T { X m } = ∑ m = 1 M x m. (4).
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The z-transformation is a linear transformation whereby the transformed mean is 0 and the standard deviation is 1.
Since the DFT is a linear transformation, averaging the Fourier-transformed time series is equivalent to performing a Fourier transformation on the average of the time series.
One of the underlying assumptions of PCA is linearity, such that the feature space is a linear transformation of the original data.
In (1.4), is a linear transformation.
Let L : ℝn+1→ ℝ n be a linear transformation.
However, is a linear transformation, moreover; it is obviuos that whenever and hence is injective.
Let and be fixed complex numbers with and let be a linear transformation defined by (4.1).
Moreover, it is clear that L is a linear transformation and (x=0) whenever (L x)=0).
Let M ∈ N ∖ { 0 } and L : R n → R M be a linear transformation.
Furthermore, it is obvious that L is a linear transformation and (x=0) whenever (L x)=0).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com