linear

中文： 线性

1. Having the form of a line; straight or roughly straight; following a direct course.
2. Of or relating to lines.
3. Made, or designed to be used, in a step-by-step, sequential manner. · a linear medium
4. Long and narrow, with nearly parallel sides.
5. Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia · 4x#43;5y#43;#92;frac#123;1#125;#123;2#125;z is a linear polynomial, but 4xy#43;#92;frac#123;1#125;#123;2#125;z and 4x#43;z² are not.
6. Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia · The graph of the linear equation y#61;ax#43;b is a straight line with slope a and y-intercept b
7. An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia · The map f#58;#92;mathbb#123;R#125;³#92;to#92;mathbb#123;R#125;² taking (x,y,z)#92;mapsto(x#43;y#43;z,x-y#43;3z) is a linear map.
8. A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia