MATRIX TRANSPOSITION Meaning and
Definition
-
Matrix transposition is a mathematical operation that involves interchanging the rows and columns of a given matrix, resulting in a new matrix. It is also commonly referred to as matrix transpose.
In a matrix, rows are horizontal groups of elements, and columns are the vertical groups. The transpose of a matrix is obtained by swapping its rows with its columns. Each element in the original matrix retains the same position in the transposed matrix, but its row and column indices are interchanged.
For example, given an original matrix A with dimensions m x n, the resulting transposed matrix, denoted as A^T, will have dimensions n x m. This implies that the number of rows in the original matrix becomes the number of columns in the transposed matrix, and vice versa.
Matrix transposition is a fundamental operation used in many fields such as linear algebra, computer science, and data analysis. It can aid in solving systems of linear equations, computing matrix products, and representing data in a different orientation. Transposed matrices often possess useful properties, such as being easier to work with in certain calculations or revealing symmetry or patterns that may be present in the original matrix.
In summary, matrix transposition involves exchanging the rows and columns of a matrix to obtain a new matrix with dimensions opposite to the original.
Common Misspellings for MATRIX TRANSPOSITION
- natrix transposition
- katrix transposition
- jatrix transposition
- mztrix transposition
- mstrix transposition
- mwtrix transposition
- mqtrix transposition
- marrix transposition
- mafrix transposition
- magrix transposition
- mayrix transposition
- ma6rix transposition
- ma5rix transposition
- mateix transposition
- matdix transposition
- matfix transposition
- mattix transposition
- mat5ix transposition
- mat4ix transposition
Etymology of MATRIX TRANSPOSITION
The word "matrix" dates back to the mid-19th century and is derived from the Latin word "matrix" meaning "womb" or "breeding female". It originally referred to a breeding place or a mold in biology. In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions.
The term "transposition" is derived from the Latin word "transponere", which means "to place across" or "to transfer". It refers to the action of exchanging positions or changing the order of elements or terms.
So, "matrix transposition" is a combination of these two terms, where "matrix" refers to a mathematical concept of an array, and "transposition" indicates the action of exchanging positions or changing the order of elements within that array.
