About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 169. Chapters: Matrix (mathematics), Rotation matrix, Water retention on mathematical surfaces, Magic square, Gamma matrices, DE-9IM, Orthogonal matrix, List of matrices, Manin matrix, Positive-definite matrix, Invertible matrix, Triangular matrix, Cabibbo-Kobayashi-Maskawa matrix, Jones calculus, Diagonalizable matrix, Pauli matrices, Kernel (matrix), Hadamard's maximal determinant problem, Jacobian matrix and determinant, Skew-symmetric matrix, Givens rotation, Hadamard matrix, Wigner D-matrix, Levinson recursion, Permutation matrix, Covariance matrix, Supermatrix, Transformation matrix, Matrix chain multiplication, Bicomplex number, Substitution matrix, Corner transfer matrix, Hessian matrix, Block matrix, Unimodular matrix, Pascal matrix, Transpose, Adjacency matrix, Householder transformation, Column space, Hierarchical matrix, Condition number, Normal matrix, S-matrix, Conference matrix, Weyl-Brauer matrices, Toeplitz matrix, Sample mean and sample covariance, Vandermonde matrix, Row space, Higher-dimensional gamma matrices, Circulant matrix, Stochastic matrix, Cartan matrix, DFT matrix, Incidence matrix, Conjugate transpose, Paley construction, Nilpotent matrix, Hermitian matrix, Symplectic matrix, Diagonally dominant matrix, Matrix group, Network operator matrix, Hasse-Witt matrix, Hat matrix, Leslie matrix, Birkhoff polytope, Design matrix, Row vector, Bezout matrix, Laplacian matrix, Row equivalence, Gramian matrix, Hilbert matrix, Logical matrix, Generalized permutation matrix, BLOSUM, Matrix similarity, Hurwitz matrix, Centrosymmetric matrix, Doubly stochastic matrix, Vectorization (mathematics), Matrix representation, Cauchy matrix, Identity matrix, Companion matrix, Shift matrix, Quaternionic matrix, Alternating sign matrix, Centering matrix, Similarity matrix, Conductance (graph), Gell-Mann matrices, Mueller calculus, Hessenberg matrix, Complex Hadamard matrix, Column vector, Total active reflection coefficient, Skew-Hermitian matrix, Walsh matrix, P-matrix, Hamiltonian matrix. Excerpt: In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The individual items in a matrix are called its elements or entries. An example of a matrix with 2 rows and 3 columns is Matrices of the same size can be added or subtracted element by element. The rule for matrix multiplication is more complicated, and two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as . For example, the rotation of vectors in three dimensional space is a linear transformation. If R is a rotation matrix and v is a column vector (a matrix with only one column) describing the position of a point in space, the product Rv is a column vector describing the position of that point after a rotation. The product of two matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in the solution of a system of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing its determinant. For example, a square matrix has an inverse if and only if its determinant is not zero. Eigenvalues and eigenvectors provide insight into the geometry of linear transformations. Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to project a 3-dimensional image onto a 2-dimensional screen. In probability theory and...
