INVERSE OF A MATRIX. Definition. (Inverse of a Matrix). Let A be a square matrix of order n. A matrix B of order n is said to be the inverse of A if Earn Money online without investment Earn Money online from home without investment Note that the inverse of an arbitrary square matrix may … Read more
Algebric properties of Matrices. Definition. (Equality of Matrices). Two [katex]m \times n[/katex] matrices [katex]A=\left[a_{i j}\right][/katex] and [katex]B=\left[b_y\right][/katex] are equal if and only if [katex]a_y=b_y[/katex] for each i and for cach j. When A and B are equal, we write A=B. Earn Money online without investment Earn Money online from home without investment Definition. (Zero Matrix). … Read more
Matrices in machine learning The importance of study of matrices lies in the fact that many situations in both pure and applied mathematics involve rectangular arrays of numbers. In many branches of business, biological and social sciences, it is necessary to express and use a set of numbers arranged in a rectangular array. For example, … Read more
Matrices in Machine Learning Transpose of a Matrix Definition. (Transpose of a Matrix). Let [katex]A=\left[a_{i j}\right][/katex] be an [katex]m \times n[/katex] matrix over a field F. The transpose of A, denoted by [katex]A^T[/katex], is an [katex]n \times m[/katex] matrix obtained by interchanging rows and columns of A. Thus [katex]A^T=\left[b_{i j}\right][/katex], where [katex]b_{i j}=a_{j i}[/katex]. In … Read more
Minor and Cofactor of a Matrix Let A be a square matrix of order n. The matrix obtained from A by deleting its ith row and jth column is again a matrix [katex]M_{ij}[/katex] of order n-1 . [katex]M_{ij}[/katex] is called the ijth minor of [katex]A^1[/katex]. Let [katex]M_{i j}[/katex] be the ijth minor of a square … Read more
DETERMINANT OF A SQUARE MATRIX The reader may be fimiliar with the concept of determinants. This concept played a basic role in the solution of systems of linear equations before the use of matrices and computers. The use of determinants is becoming less and less with every passing day. Neverthless determinants still play an important … Read more
Elementary Column Operations of a Matrix. The following operations on a matrix A are called elementry column operations. On applying an elementary column operation to the identity matrix , we obtain a corresponding column matrix, which is non singular. Earn Money online without investment Earn Money online from home without investment Column equivalent to of … Read more
ELEMENTARY ROW OPERATIONS OF A MATRIX Here we will discuss about the elementry row operations. The whole data was carefully typed. If you found any mistake then comment please. Earn Money online without investment Earn Money online from home without investment Consider the identity matrix The matrices have been obtained from [katex]I_3[/katex] by the following … Read more
An Echelon Form of a Matrix Definition. An [katex]m \times n[/katex] matrix A is said to be in (row) echelon form (or an echelon matrix) if it has the following properties: (i) All nonzero rows are above any zero rows (consisting of all zeros). (ii) The first nonzero entry in cach nonzero row is to … Read more
PARTITIONING OF MATRICES Definition. Some time we partition a matrix into blocks of elements and consider such blocks as elements of the matrix. These blocks are called sub-matrices of the original matrix and are labelled in the same manner as elements of a matrix. A matrix can be partitioned into sub-matrices in many different ways … Read more