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covariants

/koʊˈveəriənts/ /ˌkoʊˈveəriənts/

Meanings
noun
A bihomogeneous polynomial in x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

Examples :

"In advanced mathematics, students study covariants to understand how certain polynomial expressions remain unchanged even when the coordinate system is altered. "
math technical

Related Words

Illustration mathematics

mathematics noun

/mæθ(ə)ˈmætɪks/

An abstract representational system used in the study of numbers, shapes, structure, change and the relationships between these concepts.

"Mathematics helps us understand the relationship between different shapes in our daily lives. "

Illustration understand

understand verb

/ˌɞndəɹˈstand/ /(ˌ)ʌndəˈstænd/ /ˌʌndɚˈstænd/

To grasp a concept fully and thoroughly, especially (of words, statements, art, etc.) to be aware of the meaning of and (of people) to be aware of the intent of.

"My teacher explained the new math concept, and I understood it perfectly. "

Illustration coordinate

coordinate noun

/koʊˈɔːrdɪneɪt/ /koʊˈɔːrdənət/

A number representing the position of a point along a line, arc, or similar one-dimensional figure.

"The coordinate of the house on the street map was 12B. "

Illustration expressions

expressions noun

/ɪkˈspɹɛʃ.ənz/

The action of expressing thoughts, ideas, feelings, etc.

"Her expressions of gratitude after receiving the gift made everyone feel happy. "

Illustration unchanged

unchanged verb

/ʌnˈtʃeɪndʒd/

To revert or reverse a change

"The teacher un-changed the grade, reverting it back to the original score. "

Illustration invariant

invariant noun

/ɪnˈve(ə)riənt/ /ɪnˈværiənt/

An invariant quantity, function etc.

"In physics, the speed of light is an invariant, meaning it remains the same for all observers regardless of their motion. "

Illustration intrinsically

intrinsically adverb

/ɪnˈtrɪnzɪkli/ /ɪnˈtrɪnsɪkli/

In an intrinsic manner; internally; essentially.

"The project was intrinsically challenging, requiring a lot of creativity and problem-solving skills. "

Illustration covariant

covariant noun

/koʊˈveəriənt/ /koʊˈværiənt/

A bihomogeneous polynomial in x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

"Because calculating the covariant for higher-degree polynomials is computationally intensive, researchers often rely on specialized software to find them efficiently. "

Illustration polynomial

polynomial noun

/ˌpɑːlɪˈnoʊmiəl/ /ˌpɑlɪˈnoʊmiəl/

(strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as an x^n + a{n-1}x^{n-1} + ... + a_0 x^0.

"In math class, we learned that `3x² + 2x - 5` is a simple example of a polynomial. "

Illustration transformations

transformations noun

/ˌtrænsfərˈmeɪʃənz/ /ˌtrænzfərˈmeɪʃənz/

The act of transforming or the state of being transformed.

"The caterpillar's transformations into a butterfly are a beautiful example of nature's power. "

Illustration homogeneous

homogeneous adjective

/ˌhɒ.mə(ʊ)ˈdʒiː.nɪəs/ /ˌhoʊ.moʊˈdʒiː.njəs/

Of the same kind; alike, similar.

"The students in the class were a homogeneous group; they all seemed to have similar study habits. "

Illustration coefficients

coefficients noun

/ˌkoʊɪˈfɪʃənts/ /ˌkoʊəˈfɪʃənts/

A constant by which an algebraic term is multiplied.

"In the equation 3x + 2y = 7, the numbers 3 and 2 are the coefficients. "