# What is Quadratic Form in Math?

recently, finally learned what Quadratic form is.

quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,

4*x^2 + 2*x*y - 3*y^2is a quadratic form in the variables x and y.

(and Homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, `x^5 + 2 x^3 y^2 + 9 x y^4`

is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5.)

you hear about quadratic form all the time. Though, i don't know why is it significant. Is there something about them that makes them fundamental? (as in “given structure X, it is the {least, most} something?”) Or is it something happens to be a calculational convenience?

- the Nature of Associative Property of Algebra
- The Geometric Significance of Complex Conjugate
- Multiplication and Multiplicative Identity
- The Significance of Complex Numbers: Frobenius Theorem
- Euler Angles And Gimbal Lock
- Reading Notes on The Shapes of Space
- Klein Bottle Checker Board Paradox
- Learning Notes Of Symmetric Space and Differential Geometry Topics
- Reading Notes on Tilings and Patterns
- Reading Notes On Nicolas Bourbaki

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