Multilinear polynomial
Multilinear polynomials are like big puzzles made up of smaller puzzles. Let's start with a simple puzzle: 2x. This puzzle has two pieces: the number 2 and the variable x.
But now, let's make a bigger puzzle: 2x + 3y. This puzzle has two smaller puzzles inside of it: 2x and 3y. These smaller puzzles only involve one variable each (either x or y), so we call them "linear."
A multilinear polynomial is a puzzle that has multiple linear puzzles inside of it. For example: 2x + 3y + 4z. This puzzle has three smaller puzzles inside of it: 2x, 3y, and 4z. Each of these smaller puzzles only involves one variable, so they are linear. But together, they make up a bigger puzzle called a multilinear polynomial.
Multilinear polynomials can get even more complex with even more puzzles inside of them, but they will always be made up of linear puzzles involving different variables.
But now, let's make a bigger puzzle: 2x + 3y. This puzzle has two smaller puzzles inside of it: 2x and 3y. These smaller puzzles only involve one variable each (either x or y), so we call them "linear."
A multilinear polynomial is a puzzle that has multiple linear puzzles inside of it. For example: 2x + 3y + 4z. This puzzle has three smaller puzzles inside of it: 2x, 3y, and 4z. Each of these smaller puzzles only involves one variable, so they are linear. But together, they make up a bigger puzzle called a multilinear polynomial.
Multilinear polynomials can get even more complex with even more puzzles inside of them, but they will always be made up of linear puzzles involving different variables.
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