MATRIX PRODUCT Meaning and
Definition
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Matrix product refers to the operation of multiplying two matrices together to obtain a new matrix. It is a fundamental mathematical operation used in linear algebra that combines the elements of two matrices to form a resulting matrix.
In order for matrix product to be defined, the number of columns in the first matrix must match the number of rows in the second matrix. If this condition is not met, the product is undefined.
The resulting matrix from the matrix product operation is obtained by multiplying each element of a row from the first matrix with the corresponding element of a column from the second matrix, and summing up the products. The result is then placed in the corresponding position of the resulting matrix.
The size of the resulting matrix is determined by the number of rows in the first matrix and the number of columns in the second matrix. If the first matrix has dimensions m x n and the second matrix has dimensions n x p, then the resulting matrix will have dimensions m x p.
Matrix product is important in various areas such as physics, engineering, computer science, and economics, as it allows for the manipulation and transformation of data represented by matrices. It is used in solving systems of linear equations, calculating transformation matrices for geometric operations, data compression, and many other applications.
Etymology of MATRIX PRODUCT
The word "matrix" is derived from the Latin word "mātrix" which means "womb" or "source" and it was used in various senses in Middle English before its mathematical usage. In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The term "product" comes from the Latin word "productus" which means "multiplied" or "produced". In the context of matrices, a matrix product refers to the operation of multiplying two matrices together. The combination of "matrix" and "product" thus refers to the result of performing the multiplication operation on matrices.
