Eigenvalue in a sentence
Synonym: value.
Meaning: A scalar value associated with a linear transformation; often used in mathematics and physics.
(1) The unitary matrix has only one eigenvalue.
(2) Factor out the eigenvalue to find the eigenvector.
(3) The eigenvalue of a singular matrix is always zero.
(4) The eigenvalue of a symmetric matrix is always real.
(5) The eigenvalue of a non-singular matrix is never zero.
(6) The eigenvalue of a matrix can be repeated or distinct.
(7) The eigenvalue of a square matrix can be real or complex.
(8) The eigenvalue of a matrix can be used to classify its types.
(9) The eigenvalue of a matrix can be used to calculate its rank.
(10) The eigenvalue of a skew-symmetric matrix is always imaginary.
Eigenvalue sentence
(11) The eigenvalue of a matrix can be used to calculate its trace.
(12) The eigenvalue of a matrix can be used to find its eigenvectors.
(13) The eigenvalue of a matrix can be used to calculate its inverse.
(14) The eigenvalue of a matrix can be used to determine its stability.
(15) Matrix inversion is a crucial step in solving eigenvalue problems.
(16) Eigen provides efficient algorithms for solving eigenvalue problems.
(17) Diagonalising a matrix is a key step in solving eigenvalue problems.
(18) The diagonalizing process is crucial in solving eigenvalue problems.
(19) The eigenvalue of a matrix can be used to calculate its determinant.
(20) The eigenvalue of a matrix can be used to calculate its eigenvalues.
Eigenvalue make sentence
(21) The eigenvalue of a matrix can be used to calculate its eigenspaces.
(22) Factorize beside the eigenvalue to find the eigenvector of a matrix.
(23) The eigenvalue of a diagonal matrix is equal to its diagonal entries.
(24) The eigenvalue of a matrix can be used to calculate its eigenvectors.
(25) The eigenvalue of a matrix can be used to calculate its Frobenius norm.
(26) The eigenvalue of a matrix can be used to calculate its singular values.
(27) The eigenvalue of a matrix can be used to calculate its spectral radius.
(28) The eigenvalue of a matrix can be used to calculate its power iteration.
(29) The eigenvalue of a matrix can be used to calculate its condition number.
(30) The eigenvalue of a matrix can be used to analyze its spectral properties.
Sentence of eigenvalue
(31) The eigenvalue of a matrix can be used to calculate its eigendecomposition.
(32) The eigenvalue of a matrix can be computed using the characteristic equation.
(33) The eigenvalue of a matrix can be used to calculate its principal components.
(34) The eigenfunction of a linear operator satisfies a specific eigenvalue equation.
(35) The eigenvalue of a matrix determines its behavior under linear transformations.
(36) The eigenvalue of a matrix can be found by solving a system of linear equations.
(37) The eigenfunction of a self-adjoint operator is associated with a real eigenvalue.
(38) The eigenfunction of a self-adjoint operator is associated with a unique eigenvalue.
(39) The eigenstates of a degenerate system are the states that have the same eigenvalue.
(40) The eigenfunctions of a linear operator are the solutions to its eigenvalue equation.
Eigenvalue meaningful sentence
(41) The orthonormality of a set of vectors is a crucial aspect in solving eigenvalue problems.
(42) The eigenfunction of a symmetric differential operator is associated with a real eigenvalue.
(43) The eigenfunction of the Laplace operator is a solution to the corresponding eigenvalue problem.
(44) The eigenvector with the largest eigenvalue of a covariance matrix represents the direction of maximum variance in a dataset.
(45) The eigenvector with the largest eigenvalue of a correlation matrix represents the direction of maximum correlation in a dataset.
(46) The eigenvector with the smallest eigenvalue of a matrix is often associated with the least significant feature or principal component.
(47) The eigenvector corresponding to the largest eigenvalue of a matrix is often associated with the most significant feature or principal component.
Eigenvalue meaning
Eigenvalue is a mathematical term that refers to a scalar value that is associated with a particular linear transformation. It is a crucial concept in linear algebra and is used extensively in various fields such as physics, engineering, and computer science. If you are new to the concept of eigenvalues, it can be challenging to understand how to use it in a sentence. In this article, we will provide you with some tips on how to use the word eigenvalue in a sentence. Tip
1. Understand the meaning of eigenvalue Before you start using the word eigenvalue in a sentence, it is essential to understand its meaning. Eigenvalue is a scalar value that is associated with a particular linear transformation. It is a value that remains unchanged even after the transformation is applied.
For example, if you have a matrix A and a vector x, the eigenvalue of A is a scalar value ? that satisfies the equation Ax = ?x. Once you understand the meaning of eigenvalue, you can use it in a sentence more effectively. Tip
2. Use eigenvalue in a mathematical context Eigenvalue is a mathematical term, and it is best used in a mathematical context.
For example, you can use eigenvalue in a sentence when discussing linear transformations, matrices, or vectors. Here are some examples: - The eigenvalue of the matrix A is 3. - The eigenvectors of the linear transformation T are orthogonal. - The eigenvalue problem is a fundamental concept in linear algebra. Tip
3. Use eigenvalue in a scientific context Eigenvalue is not only used in mathematics but also in various scientific fields such as physics, engineering, and computer science. If you are writing a scientific paper or discussing a scientific concept, you can use eigenvalue in a sentence. Here are some examples: - The eigenvalue of the Hamiltonian operator is used to calculate the energy levels of a quantum system. - The eigenvalue of a structural matrix is used to determine the stability of a building. - The eigenvalue decomposition is a common technique used in signal processing. Tip
4. Use eigenvalue in a practical context Eigenvalue may seem like a complex mathematical concept, but it has practical applications in various fields. If you are discussing a practical application of eigenvalue, you can use it in a sentence. Here are some examples: - The eigenvalue of a covariance matrix is used to determine the principal components of a dataset. - The eigenvalue of a correlation matrix is used to determine the strength of the relationship between variables. - The eigenvalue of a Laplacian matrix is used to determine the connectivity of a network.
In conclusion, eigenvalue is a mathematical term that is used extensively in various fields. To use eigenvalue in a sentence effectively, it is essential to understand its meaning and use it in a mathematical, scientific, or practical context. By following these tips, you can use eigenvalue in a sentence with confidence and clarity.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Eigenvalue. They do not represent the opinions of TranslateEN.com.