Linear Transformation

Transformation

• A transformation, function, or mapping, T maps an input x to an output y
  • Mathematical notation: T: x -> y
• Domain: Set of all the possible values of x (정의역)
• Co-domain: Set of all the possible values of y (공역)
• Image: a mapped output y, given x
• Range: Set of all the output values mapped by each x in the domain (치역)
• Note: the output mapped by a particular x is uniquely determined.

Linear Transformation

• Definition: A transformation (or mapping) T is linear if: I. T(cu + dv) = cT(u) + dT(v) for all u, v in the domain of T and for all scalars c and d
• Simple example: T: x -> y, T(x) = y = 3x

Linear Transformation in Neural Networks

• Fully-connected layers (linear layer)
• Example: Image with 4 pixels and 3 classes (cat/dog/ship)