For the matrix A at the beginning of this section, verify that A*inv(A)=inv(A)*A=eye(3). The n × n identity matrix I is represented in MATLAB by eye(n). If A is a square matrix with |A| = 0, then inv(A) represents the inverse of A, denoted in mathematics by A −1. The magnitude or Euclidean norm of the vector v, given by Hence, if you need to input the column vector It is formed by interchanging the rows and columns. Similarly, A.*B is not matrix multiplication but merely multiplies the corresponding positions in the two matrices.ĭet(A) is the determinant of A, written |A|.Ī' is the transpose of A and is written in mathematics as A T. Note: A.^2 does not square the matrix but squares each element in the matrix. However, B+C and C*A produce error messages. Hence calculate after the prompt D=2*A-B, F=A*B, G=A*C, Asq=A^2. Providing they have compatible shapes they can be multiplied using the established rules for matrix multiplication. Providing matrices have the same shape they can be added or subtracted. Hence A(:,2) is column number 2 in the matrix A while is the first row of B. The comma separates the row number(s) from the column number(s).Ī single colon “:” before the comma means “take all rows”, whereas a single colon after the comma means “take all columns”. The element A(i,j) is in the i th row and j th column. For example, run the following M-file mat.m: To construct a matrix with m rows and n columns (called an “m by n matrix”, written m×n matrix), each row in the array ends with a semicolon. Hi, I have to convert a matrix in one column/row vector composed of all the rows of the original matrix. Since you desire the elements to be populated by rows, a trick is to simply transpose the result. Therefore, just using reshape by itself will place the elements in the columns. The matrix is created in column-major order. But you are aware that a rectangular array represents a matrix and a single array column represents a column vector. reshape transforms a vector into a matrix of a desired size. Each array that was discussed in Section 4 was, in effect, a row vector or row matrix.
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