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In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and...

matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must...

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...

multiplied by another matrix to yield the identity matrix. Invertible matrices are the same size as their inverse. The inverse of a matrix represents...

transpose of z . {\displaystyle \mathbf {z} .} Positive semi-definite matrices are defined similarly, except that the scalars x T M x {\displaystyle \mathbf...

distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory...

square matrices have the identity matrix as their product exactly when they are the inverses of each other. When n × n {\displaystyle n\times n} matrices are...

In linear algebra, linear transformations can be represented by matrices. If T {\displaystyle T} is a linear transformation mapping R n {\displaystyle...

Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always...

&\cdot &X&\cdot &X&\\\end{bmatrix}}} Matrices with reasonably small upper and lower bandwidth are known as band matrices and often lend themselves to simpler...

article. Rotation matrices are square matrices, with real entries. More specifically, they can be characterized as orthogonal matrices with determinant...

below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By...

lines, which break it up, or partition it, into a collection of smaller matrices. For example, the 3x4 matrix presented below is divided by horizontal and...

normal matrices are real symmetric (or skew-symmetric) matrices (e.g. covariance matrices) and Hermitian matrices (or skew-Hermitian matrices). See spectral...

orthogonal matrices, under multiplication, forms the group O(n), known as the orthogonal group. The subgroup SO(n) consisting of orthogonal matrices with determinant...

symmetric}}\iff A=A^{\textsf {T}}.} Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix...

outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example...

the sequence of principal (upper-leftmost) minors (determinants of sub-matrices) of the Hessian; these conditions are a special case of those given in...

operator enters text on a 90-character keyboard. The machine assembles matrices, or molds for the letter forms, in a line. The assembled line is then cast...

numbers, the analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve...