hermitian matrix: meaning, definition, pronunciation and examples
Low (Technical)Formal, Technical, Academic
Quick answer
What does “hermitian matrix” mean?
A square matrix that is equal to its own conjugate transpose.
Audio
Pronunciation
Definition
Meaning and Definition
A square matrix that is equal to its own conjugate transpose.
A fundamental concept in linear algebra and quantum mechanics, where its eigenvalues are always real numbers, making it crucial for modeling physical systems and in spectral theory.
Dialectal Variation
British vs American Usage
Differences
Spelling of 'matrix' plural: 'matrices' is universal. No significant difference in usage.
Connotations
Exclusively technical. No regional connotations.
Frequency
Used with identical frequency in UK and US academic/technical contexts.
Grammar
How to Use “hermitian matrix” in a Sentence
The matrix A is Hermitian.A Hermitian matrix has...Verify that the matrix is Hermitian.Vocabulary
Collocations
Examples
Examples of “hermitian matrix” in a Sentence
adjective
British English
- The operator was Hermitian.
- We require a Hermitian form.
American English
- The matrix needs to be Hermitian.
- This ensures the Hamiltonian is Hermitian.
Usage
Meaning in Context
Business
Never used.
Academic
Core term in mathematics, physics, and engineering courses.
Everyday
Never used.
Technical
Essential in quantum mechanics, signal processing, and linear algebra libraries in programming.
Vocabulary
Synonyms of “hermitian matrix”
Neutral
Weak
Vocabulary
Antonyms of “hermitian matrix”
Watch out
Common Mistakes When Using “hermitian matrix”
- Misspelling as 'Hermitian' (one 'm').
- Confusing with 'Hamiltonian' (related to energy).
- Forgetting the requirement for complex entries.
FAQ
Frequently Asked Questions
Yes. For real matrices, the conjugate transpose is simply the transpose, so a real symmetric matrix is a special case of a Hermitian matrix.
They represent observable physical quantities (like position or momentum) because their eigenvalues (the possible measurement results) are real numbers.
'Symmetric' is typically used for real matrices (A = A^T). 'Hermitian' is the complex extension (A = A^H, where H denotes conjugate transpose).
Yes, and it often does. The key is that the entries on the main diagonal must be real numbers, and off-diagonal entries must be complex conjugates of each other across the diagonal.
A square matrix that is equal to its own conjugate transpose.
Hermitian matrix is usually formal, technical, academic in register.
Hermitian matrix: in British English it is pronounced /hɜːˈmɪ.ʃən ˈmeɪ.trɪks/, and in American English it is pronounced /hɝːˈmɪ.ʃən ˈmeɪ.trɪks/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
A Hermitian matrix is HONEST: Its Honest Own conjugate transpose equals its Normal Self Exactly.
Conceptual Metaphor
Mathematical self-reflection (like a mirror for complex numbers).
Practice
Quiz
What is a key property of a Hermitian matrix?