What is Symmetric Matrix? A symmetric matrix in linear algebra is a square matrix that remains unaltered when its transpose is calculated. That means, a matrix whose transpose is equal to …

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A is symmetric A = A T . {\displaystyle A {\text { is symmetric}}\iff A=A^ {\textsf {T}}.} Because …

Nov 18, 2025 · Symmetric and Skew Symmetric Matrices are types of square matrices based on the relation between a matrix and its transpose. These matrices are one of the most used …

We explain what a symmetric matrix is. Also, you'll find examples of symmetric matrices and all the properties of this type of matrices.

A matrix is symmetric if and only if it is orthogonally diagonalisable. Note that this also establishes the property that for each eigenvalue of a symmetric matrix the geometric multiplicity equals …

A symmetric matrix is a special type of square matrix in linear algebra. It's called "symmetric" because it remains the same when you swap its rows and columns.

A symmetric matrix is a special type of square matrix that is equal to its own transpose. In simple terms, if you swap the rows and columns of the matrix, you get the exact same matrix back.

A symmetric matrix may be recognized visually: The entries that are symmetrically positioned with respect to the main diagonal are equal as shown in the example below of a symmetric matrix. …

Symmetric Matrix with clear definitions, examples, and explanations. Perfect for students and math enthusiasts!

Dec 3, 2025 · A symmetric matrix is a square matrix that satisfies A^ (T)=A, (1) where A^ (T) denotes the transpose, so a_ (ij)=a_ (ji). This also implies A^ (-1)A^ (T)=I, (2) where I is the …