Eigenvalues and eigenvectors and Stress (mechanics)

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Difference between Eigenvalues and eigenvectors and Stress (mechanics)

Eigenvalues and eigenvectors vs. Stress (mechanics)

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.

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Finite element method

The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.

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Geology

Geology (from the Ancient Greek γῆ, gē, i.e. "earth" and -λoγία, -logia, i.e. "study of, discourse") is an earth science concerned with the solid Earth, the rocks of which it is composed, and the processes by which they change over time.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Solid mechanics

Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

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Stress (mechanics)

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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