A linear vector function is a mathematical function that maps a vector input to a vector output. It follows the properties of linearity, meaning that the function preserves vector addition and scalar multiplication.
A linear vector function is typically represented using matrix notation, where the input vector is multiplied by a transformation matrix to produce the output vector. It can also be represented using a system of linear equations.
A linear vector function preserves the properties of linearity, while a non-linear vector function does not. This means that a linear vector function will always produce a straight line or plane when graphed, while a non-linear vector function can produce curved or non-planar shapes.
Yes, a linear vector function can have multiple inputs, but it must also have multiple outputs in order to preserve linearity. This would typically be represented using a vector of inputs and a vector of outputs, and a transformation matrix that maps between them.
Linear vector functions have many applications in fields such as physics, engineering, and computer graphics. They are used in systems of equations to model linear relationships between variables, in transformations to manipulate and analyze data, and in computer graphics to create 3D objects and animations.