homogeneous polynomial Sentence Examples
- In algebra, a homogeneous polynomial is an expression consisting of terms where each term has the same total degree.
- A homogeneous polynomial of degree 2 is also known as a quadratic form.
- To determine if a polynomial is homogeneous, one must check if each term's total degree is consistent throughout the expression.
- Homogeneous polynomials are important in fields like geometry and physics for describing symmetrical structures.
- A common example of a homogeneous polynomial is \(x^2 + 2xy + y^2\), where each term has a degree of 2.
- Homogeneous polynomials are often used in multivariable calculus to define surfaces and curves.
- The study of homogeneous polynomials is integral to understanding projective geometry.
- Homogeneous polynomials play a crucial role in solving systems of equations and linear algebra problems.
- A homogeneous polynomial of degree \(n\) has terms where the sum of the exponents of each variable is \(n\).
- Homogeneous polynomials are extensively studied in algebraic geometry for their applications in defining algebraic varieties.
homogeneous polynomial Meaning
Wordnet
homogeneous polynomial (n)
a polynomial consisting of terms all of the same degree
Synonyms & Antonyms of homogeneous polynomial
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FAQs About the word homogeneous polynomial
a polynomial consisting of terms all of the same degree
No synonyms found.
No antonyms found.
In algebra, a homogeneous polynomial is an expression consisting of terms where each term has the same total degree.
A homogeneous polynomial of degree 2 is also known as a quadratic form.
To determine if a polynomial is homogeneous, one must check if each term's total degree is consistent throughout the expression.
Homogeneous polynomials are important in fields like geometry and physics for describing symmetrical structures.
