Definitions
- Describing a mathematical matrix that is positive semidefinite, meaning all eigenvalues are non-negative. - Referring to a type of optimization problem in which the objective function is a linear combination of semidefinite matrices. - Talking about a type of cone in a vector space that includes all positive semidefinite matrices.
- Describing a mathematical matrix that is indefinite, meaning it has both positive and negative eigenvalues. - Referring to a type of integral that does not converge or diverge. - Talking about a type of pronoun that does not refer to a specific person or thing.
List of Similarities
- 1Both words are used in mathematics.
- 2Both words describe properties of matrices.
- 3Both words have multiple meanings depending on the context.
What is the difference?
- 1Meaning: Semidefinite refers to a matrix with non-negative eigenvalues, while indefinite refers to a matrix with both positive and negative eigenvalues.
- 2Optimization: Semidefinite is used in semidefinite programming, while indefinite is not typically used in optimization problems.
- 3Convergence: Semidefinite matrices are guaranteed to converge, while indefinite integrals may or may not converge.
- 4Pronouns: Indefinite can also refer to a type of pronoun, while semidefinite does not have any other meanings beyond mathematics.
- 5Formality: Semidefinite is a technical term used in mathematics and engineering, while indefinite has broader usage in everyday language.
Remember this!
Semidefinite and indefinite are both terms used in mathematics, but they have different meanings and applications. Semidefinite refers to a matrix with non-negative eigenvalues, often used in optimization problems, while indefinite refers to a matrix with both positive and negative eigenvalues or an integral that does not converge or diverge. Additionally, indefinite can also refer to a type of pronoun in language.
