Are you in search of an article from the world of mathematics that is both interesting and informative? Well, your search is over now as you have come to the right page where you get engaging and enlightening articles to read. Today’s article is going to be on matrices. You must have read about them earlier. However, today’s reading will add to your existing knowledge. Through this article, you will learn the definition, application, calculation, and multiplication of transpose in matrices. Make sure you go through the entire article as this article will definitely give you some interesting takeaways that will help you update your knowledge of matrices. Now, without any further ado, let’s start reading with the definition of the transpose of a matrix.
What Is The Meaning Of The Transpose Of A Matrix?
- The transpose of a matrix is one of the standard methods used for matrix transformation in matrix concepts across linear algebra.
- The transpose of a matrix is acquired by adjusting the rows into columns and columns into rows for a given matrix.
- In linear algebra, the transpose of a matrix is an operator that reverses a matrix over its diagonal by switching the row and column indices of matrix B and producing another matrix.
- The transpose of a matrix B is often marked by either B’ or BT. Occasionally, they are also denoted as Btr or Bt.
- Suppose a matrix named ‘B’ is of order m×n, then the transpose of a new matrix named ‘B’ is of the order n×m.
- There are various applications of the transpose of a matrix, from image processing, signal modulation/demodulation, geographic information systems, and statistical programming to social network analysis.
- The knowledge of the transpose of a matrix is especially useful in applications where inverse and adjoint of matrices are to be obtained.
How To Find The Transpose Of A Matrix?
- Step 1: When you wish to find out the transpose of a matrix, firstly, interchange the rows and columns of a matrix.
- Step 2: Write the elements of the rows as columns and then write the elements of a column as rows.
For example – You have been given a fixed matrix of 3×6. It simply means that there are 3 rows and 6 columns. Now, to find the transpose of a matrix, the elements present in the first row of the matrix are written in the first column of the new matrix. Likewise, the elements in the second row of the given matrix are written in the second column of the new matrix. Hence, the order of the new matrix becomes 6×3, as it has 6 rows and 3 columns.
How To Multiply A Matrix?
- To perform a multiplication of matrix, you have to realize that matrix multiplication is not commutative.
- To multiply a matrix by a single number is easy. The number is referred to as the scalar, therefore, this method is called scalar multiplication.
- However, to multiply a matrix by another matrix we are required to do the “dot product” of rows and columns.
- The “dot product” is where we multiply corresponding members, then add them up.
- The number of columns of the 1st matrix must nr equal to the number of rows of the 2nd matrix.
- As a result, you will have the same number of rows as the 1st matrix, and the same number of columns as the 2nd matrix.
We hope this article proved to be worthy of reading. Keep connected to us for more interesting and informational content from the world of mathematics.