Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 adjective Linear with respect to each of two variables or positions. Used of functions or equations.
from The Century Dictionary.
 Consisting of or having reference to two lines: as, bilinear coördinates.
 Linear in two ways. Thus the form
Σ _{i}Σ _{j} a_{ij} x_{i} y_{j} is a bilinear form, that is, lineolinear.
from the GNU version of the Collaborative International Dictionary of English.
 adjective (Math.) Of, pertaining to, or included by, two lines.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics, of a function in two variables
Linear (preservinglinear combinations ) in eachvariable .  noun mathematics A bilinear
function
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adjective linear with respect to each of two variables or positions
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The far right is the 720 export from 1080i original from iMovie, and I found out that the closest effect was seen when I resized 1080i image to 720 using 'bilinear' interpolation, very cheap way to resize an image.

However, the polarization identities will allow you to recover the bilinear function from the quadratic one.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

However, the polarization identities will allow you to recover the bilinear function from the quadratic one.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

However, the polarization identities will allow you to recover the bilinear function from the quadratic one.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

EDIT: A note from The Unapologetic Mathematician that I should add: the metric tensor is a bilinear function of two vectors at a given point, while the line element is a quadratic function of a single vector.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

EDIT: A note from The Unapologetic Mathematician that I should add: the metric tensor is a bilinear function of two vectors at a given point, while the line element is a quadratic function of a single vector.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Then in matrix form the metric looks like diag ( 1,1,1,1) as a bilinear form.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

They all use bilinear filtering rather than something reasonable like bicubic or lanczos or, really, anything that looks decent.

From the density matrix point of view, state vectors are a kluge that is done so that a quantum state can be converted from its natural bilinear condition, to an unnatural, but mathematically convenient linear one.

I realize this is “raw” data, but we also need to be aware that Hansen99 used 1950 as the hinge point for his bilinear adjustment.
A First Look at the USHCN Quality Classification « Climate Audit
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