Diagonalizable in a sentence
Synonym: diagonal, transformable.
Meaning: Referring to a matrix that can be transformed into a diagonal matrix; important in linear algebra.
(1) Diagonalizable matrices have distinct eigenvalues.
(2) Diagonalizable matrices are commonly used in linear algebra.
(3) The unitarily diagonalizable matrices have distinct eigenvalues.
(4) The theorem states that every symmetric matrix is diagonalizable.
(5) A matrix is diagonalizable if and only if it has n distinct eigenvalues.
(6) Diagonalizable matrices have a special form that simplifies calculations.
(7) A diagonalizable matrix can be easily inverted by diagonalizing it first.
(8) The diagonalizable nature of the matrix allows for efficient computations.
(9) The matrix is diagonalizable if and only if it has n distinct eigenvalues.
(10) The diagonalizable property of a matrix is a key concept in linear algebra.
Diagonalizable sentence
(11) The mathematician's theorem proved the existence of diagonalizable matrices.
(12) A matrix is diagonalizable if and only if it is similar to a diagonal matrix.
(13) The diagonalizable property of a matrix is closely related to its eigenvalues.
(14) A matrix is diagonalizable if and only if it has a complete set of eigenvectors.
(15) The eigenvalues of a diagonalizable matrix are the entries on its main diagonal.
(16) The diagonalizable nature of the matrix simplifies the computation of its powers.
(17) The endomorphisms of a finite-dimensional vector space are always diagonalizable.
(18) A diagonalizable matrix can be easily manipulated using elementary row operations.
(19) Diagonalizable matrices have distinct eigenvalues with corresponding eigenvectors.
(20) The diagonalizable property of a matrix is a fundamental concept in matrix theory.
Diagonalizable make sentence
(21) The diagonalizable property of a matrix simplifies certain mathematical operations.
(22) Diagonalizable matrices play a crucial role in various applications of mathematics.
(23) The diagonalizable property of a matrix is a fundamental concept in linear algebra.
(24) A diagonalizable matrix can be transformed into a diagonal matrix using eigenvectors.
(25) Diagonalizable matrices have a special property that simplifies their representation.
(26) The diagonalizable property of a matrix allows for simpler calculations and analysis.
(27) A matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
(28) The diagonalizable property of a matrix can be proven using the Jordan canonical form.
(29) The diagonalizable nature of the matrix makes it suitable for certain transformations.
(30) Diagonalizable matrices have a unique factorization into eigenvalues and eigenvectors.
Sentence of diagonalizable
(31) The diagonalizable property of a matrix can be determined by examining its eigenvalues.
(32) The matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
(33) The diagonalizable property of a matrix allows for efficient diagonalization algorithms.
(34) A matrix is diagonalizable if it has a complete set of linearly independent eigenvectors.
(35) The diagonalizable property of a matrix can be used to solve systems of linear equations.
(36) The diagonalizable property of a matrix is useful in solving systems of linear equations.
(37) A diagonalizable matrix can be easily manipulated and transformed using its eigenvectors.
(38) The diagonalizable property of a matrix is closely related to its spectral decomposition.
(39) A diagonalizable matrix can be easily raised to a power by exponentiating its eigenvalues.
(40) The diagonalizable property of a matrix simplifies its computation of powers and inverses.
Diagonalizable meaningful sentence
(41) A diagonalizable matrix can be used to solve systems of linear equations more efficiently.
(42) The diagonalizable property of a matrix is a desirable characteristic in many applications.
(43) An endomorphism is said to be diagonalizable if it can be represented by a diagonal matrix.
(44) The diagonalizable property of a matrix allows for efficient computation of its exponential.
(45) The diagonalizable nature of the matrix allows for efficient computation of its determinant.
(46) A diagonalizable matrix can be easily inverted by inverting its eigenvalues and eigenvectors.
(47) A diagonalizable matrix can be transformed into a diagonal matrix by finding its eigenvectors.
(48) The diagonalizable property of a matrix simplifies its computation of determinants and traces.
(49) The eigenvalues of a diagonalizable matrix can be found by solving the characteristic equation.
(50) The diagonalizable property of a matrix is closely related to its eigenvalues and eigenvectors.
Diagonalizable sentence examples
(51) A diagonalizable matrix can be easily diagonalized by finding its eigenvectors and eigenvalues.
(52) A diagonalizable matrix can be used to represent linear transformations in a more concise form.
(53) A diagonalizable matrix can be easily manipulated and transformed using its eigendecomposition.
(54) A square matrix is diagonalizable if it has a complete set of linearly independent eigenvectors.
(55) The diagonalizable property of a matrix simplifies its computation of characteristic polynomials.
(56) The diagonalizable property of a matrix allows for easier analysis of its behavior and properties.
(57) A matrix is diagonalizable if it can be expressed as a product of diagonal and invertible matrices.
(58) A diagonalizable matrix can be used to represent linear transformations in a more efficient manner.
(59) A diagonalizable matrix can be decomposed into a product of its eigenvectors and a diagonal matrix.
(60) The diagonalizable property of a matrix allows for simpler calculations of its powers and inverses.
Sentence with diagonalizable
(61) The diagonalizable matrix can be easily transformed into a diagonal matrix using eigendecomposition.
(62) The diagonalizable property of a matrix allows for easier analysis of its stability and convergence.
(63) A diagonalizable matrix can be transformed into a diagonal matrix by finding its eigendecomposition.
(64) The matrix is diagonalizable if it can be expressed as a product of diagonal and invertible matrices.
(65) The diagonalizable property of a matrix is a desirable characteristic in many mathematical applications.
(66) A matrix is diagonalizable if it can be transformed into a diagonal matrix using similarity transformations.
(67) The spectral theorem for finitedimensional normal operators states that every such operator is diagonalizable.
(68) A diagonalizable matrix can be written as a sum of its eigenvalues multiplied by their corresponding eigenvectors.
(69) A diagonalizable matrix can be decomposed into a product of its eigenvectors and a diagonal matrix using eigendecomposition.
Diagonalizable meaning
Diagonalizable is a term used in linear algebra to describe a matrix that can be transformed into a diagonal matrix through a similarity transformation. In simpler terms, it means that a matrix can be simplified into a diagonal form, which makes it easier to work with and analyze. If you are studying linear algebra or working with matrices, it is important to understand how to use the term diagonalizable correctly in a sentence. Here are some tips to help you use this term effectively:
1. Understand the definition: Before you can use the term diagonalizable in a sentence, you need to understand what it means. Make sure you are familiar with the concept of diagonalization and how it applies to matrices.
2. Use it in context: When using the term diagonalizable in a sentence, make sure you are using it in the correct context.
For example, you might say "The matrix A is diagonalizable" to indicate that matrix A can be transformed into a diagonal matrix.
3. Be clear and concise: When using technical terms like diagonalizable, it is important to be clear and concise in your language. Avoid using overly complex sentences or jargon that might confuse your audience.
4. Provide examples: To help illustrate your point, provide examples of matrices that are diagonalizable and those that are not. This can help your audience understand the concept more clearly.
5. Use it in writing and speech: Whether you are writing a paper or giving a presentation, make sure you use the term diagonalizable consistently and correctly. This will help you communicate your ideas effectively and avoid confusion.
Overall, using the term diagonalizable correctly in a sentence requires a solid understanding of linear algebra and the concept of diagonalization. By following these tips, you can use this term effectively in your work and communicate your ideas clearly to others.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Diagonalizable. They do not represent the opinions of TranslateEN.com.