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A symmetric matrix is defined as a square matrix that is equal to its transpose. A symmetric matrix can A can therefore satisfies the condition, A = A^T. Understand the symmetric matrices using theorems and examples.
- Subtraction of Matrices
All constraints for the addition of matrices are applied to...
- Skew-symmetric Matrix
When two skew-symmetric matrices are added, then the...
- Sum
Addition of Matrices. The addition of matrices is a...
- Adjoint of a Matrix
A matrix is a rectangular array that contains numbers or...
- Transpose
The transpose of a matrix is obtained by changing the rows...
- Square Matrix
For example, matrices of orders 2x2, 3x3, 4x4, etc are...
- Inverse of Matrix
In the case of real numbers, the inverse of any real number...
- Determinant of a Matrix
But there are some tricks to find the determinants of 1x1,...
- Subtraction of Matrices
Symmetry of a 5×5 matrix. In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, is symmetric {\displaystyle A {\text { is symmetric}}\iff A=A^ {\textsf {T}}.} Because equal matrices have equal dimensions, only square matrices can be symmetric.
Symmetric matrices appear in many different contexts. In statistics the covariance matrix is an example of a symmetric matrix. In engineering the so-called elastic strain matrix and the moment of inertia tensor provide examples. The crucial thing about symmetric matrices is stated in the main theorem of this section. Theorem 8.1.1.
How do you know if a matrix is symmetric? Examples of symmetric matrices; Properties of symmetric matrices; Decomposition of a square matrix into a symmetric and an antisymmetric matrix
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Symmetric Matrices. By a team of lecturers and developers from the Delft Institute of Applied Mathematics from the TU Delft University of Technology. Have you spotted a mistake or an error on this page? Click here to tell us!
Symmetric matrices appear in geometry, for example, when introducing more general dot products v Av or in statistics as correlation matrices Cov[X k,X l] or in quantum mechanics as observables or in neural networks as learning maps x sign(Wx) or in graph theory as adjacency matrices.
