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2. Square matrix - Wikipedia

   en.wikipedia.org/wiki/Square_matrix

   The entries form the main diagonal of a square matrix. For instance, the main diagonal of the 4×4 matrix above contains the elements a 11 = 9, a 22 = 11, a 33 = 4, a 44 = 10. In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order .

3. Matrix (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Matrix_(mathematics)

   A square matrix is a matrix with the same number of rows and columns. [5] An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. The entries a ii form the main diagonal of a square matrix. They lie on the imaginary line that runs from the top left corner to the bottom ...

4. List of named matrices - Wikipedia

   en.wikipedia.org/wiki/List_of_named_matrices

   A square matrix derived by applying an elementary row operation to the identity matrix. Equivalent matrix: A matrix that can be derived from another matrix through a sequence of elementary row or column operations. Frobenius matrix: A square matrix in the form of an identity matrix but with arbitrary entries in one column below the main diagonal.

5. Determinant - Wikipedia

   en.wikipedia.org/wiki/Determinant

   In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or | A |. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.

6. Singular value decomposition - Wikipedia

   en.wikipedia.org/wiki/Singular_value_decomposition

   Consequently, if all singular values of a square matrix ⁠ ⁠ are non-degenerate and non-zero, then its singular value decomposition is unique, up to multiplication of a column of ⁠ ⁠ by a unit-phase factor and simultaneous multiplication of the corresponding column of ⁠ ⁠ by the same unit-phase factor.

7. Diagonal matrix - Wikipedia

   en.wikipedia.org/wiki/Diagonal_matrix

   More often, however, diagonal matrix refers to square matrices, which can be specified explicitly as a square diagonal matrix. A square diagonal matrix is a symmetric matrix, so this can also be called a symmetric diagonal matrix. The following matrix is square diagonal matrix: [] If the entries are real numbers or complex numbers, then it is a ...

8. Eigendecomposition of a matrix - Wikipedia

   en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

   Let A be a square n × n matrix with n linearly independent eigenvectors q i (where i = 1, ..., n).Then A can be factored as = where Q is the square n × n matrix whose i th column is the eigenvector q i of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, Λ ii = λ i.

9. Matrix exponential - Wikipedia

   en.wikipedia.org/wiki/Matrix_exponential

   The matrix exponential satisfies the following properties. [2] We begin with the properties that are immediate consequences of the definition as a power series: e 0 = I; exp(X T) = (exp X) T, where X T denotes the transpose of X. exp(X ∗) = (exp X) ∗, where X ∗ denotes the conjugate transpose of X. If Y is invertible then e YXY −1 = Ye ...