Презентация на тему Matrix

"Matrices and operations on them" PLAN: 1. Concept and types of matrices2. Тhe rows, columns, elements,     аnd the size of the matrix3. Оperations on matrices Concept and types matrix DEFINITIONS Matrix is a rectangular or square tables filled with numbers. Numbers, fills the matrix called matrix elements. TYPES OF MATRIX Rectangular matrix Column matrix Square matrix Row matrix Rows, columns, elements, and size of the matrix Priciple Numbering . Rows and columns String are numbered from top down singe number 1. Left columns are numbered right starting with number 1. Row and column 3rd row 3rd Co- lumn Size of the matrix A matrix having m rows and n Columns is called a matrix Size m by n. Matrix of size 3 for 2 (column 3, line 2) Outfit matrix of size m by n Element of the matrix Diagonal square matrix The main diagonal Secondary diagonal Triangular matrix An upper triangular matrix (below the main diagonal are zeros) Lower triangular matrix (above the main diagonal are zeros) Matrix operations Any matrix can be multiplied by the number Matrices of the same size can be аdd and subtract Matrix transposition The initial matrix 3 for 2 Transpose matrix 2 for 3 Multiplication line to column (Scalar product) Multiplication matrix for each column rows of the matrix scalar product of a column Opportunity matrix-matrix multiplication The matrix A, written left, can be multiplied by matrix B, recorded right, then and only then, when the number of columns of A equals the number of rows of the matrix B Multiplication rule matrix-matrix e ach row of the matrix of scalar multiplies left to right every column matrix C=A*B A-left matrix B-right matrix Example of matrix multiplication MULTIPLICATION COLUMN ON LINE Important types square matrix Identity matrix (size 3 x 3) Zero matrix (size 3 by 3) Property identity matrix: A • E = E • A = A THANK YOU FOR YOUR ATTENTION!