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A square matrix of order 4. 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.
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 ...
In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group GL n ( F ) when F is a field .
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.
A square matrix whose transpose is equal to its inverse is called an orthogonal matrix; ... The operation of taking the transpose is an involution (self-inverse).
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 ...
In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their ...
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.