Matrix MultiplicationDownload Wolfram Notebook The product of two matrices and is defined as (1) where is summed over for all possible values of and and the notation above uses the Einstein summation convention. The implied summation over repeated indices without the presence of an explicit sum...
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Definition 18 (Matrix Multiplication). If A = (aij) is an n × k matrix and B = (bij) is an k × m matrix, AB is the unique n × m matrix C = (cij) where c11=a11b11+a12b21+⋯+a1kbk1=∑i=1ka1ibi1,c12=a11b12+a12b22+⋯+a1kbk2=∑i=1ka1ibi2,andcuv=au1b1v+au...
4x4 Matrix Multiplication X Submit Added May 23, 2013 in Widget Gallery Send feedback|Visit Wolfram|Alpha SHARE Email Twitter Facebook More... URL EMBED Make your selections below, then copy and paste the code below into your HTML source. * For personal use only. Theme Output Type Lightbox...
//////Run example//////<seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Scalar_multiplication">Multiplymatrix by scalar</seealso>///<seealso cref="http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html">Multiplymatrix by vector</seealso>///<seeal...
k-Matrix, Matrix Cube Root, Matrix Exponential, Matrix Multiplication, Matrix Polynomial, Matrix Root, Matrix Square Root, Nilpotent Matrix, Periodic Matrix Explore with Wolfram|AlphaMore things to try: matrix operations conjugate transpose matrix power {{4,-6},{1,5}}, 2 ...
A matrix can be tested to see if it is a special unitary matrix using the Wolfram Language function SpecialUnitaryQ[m_List?MatrixQ] := (Conjugate @ Transpose @ m . m == IdentityMatrix @ Length @ m&& Det[m] == 1) The special unitary matrices are closed under multiplication and the...
The-matrices immediately give a number of important Fibonacci identities, including (3) which gives (4) (5) which gives (6) and (7) which gives (8) (Honsberger 1985, pp. 105-106). See also Explore with Wolfram|Alpha
Drazin Inverse, Gauss-Jordan Elimination, Gaussian Elimination, LU Decomposition, Matrix, Matrix 1-Inverse, Matrix Addition, Matrix Multiplication, Moore-Penrose Matrix Inverse, Nonsingular Matrix, Pseudoinverse, Singular Matrix, Strassen Formulas Explore this topic in the MathWorld classroom ...
A matrix can be tested to see if it is a special orthogonal matrix using the Wolfram Language code SpecialOrthogonalQ[m_List?MatrixQ] := (Transpose[m] . m == IdentityMatrix @ Length @ m && Det[m] == 1) The special orthogonal matrices are closed under multiplication and the inverse...