Transpose of a Matrix
The transpose of a matrix A is got by interchanging its rows and columns and is denoted by A' or A T . If A = [a i j ] m x n is a matrix of order mxn, the transpose of A = A' = [a j i ] n x m is a matrix of order n..
The transpose of a matrix A is got by interchanging its rows and columns and is denoted by A' or A T . If A = [a i j ] m x n is a matrix of order mxn, the transpose of A = A' = [a j i ] n x m is a matrix of order n..Adjoint and Inverse of a Matrix
The adjoint of a square matrix [aij] is defined as the transpose of the matrix [Aij] where Aij are the cofactors of the elements aij. Adjoint of A is denoted by adj A. Let A be a square matrix of order n. If there exists a matrix B of o..
Proof by induction that transposing a matrix does not change its determinant
Transpose of a matrix
Question : I looked it up and found that the transpose is just an exchange of the rows and columns and the complex transpose is found by taking the complex conjugates of each entry in the transposed matrix. However, what is the complex transpose of a matrix that does not have complex numbers as its entries? Would it be the same as the transpose of the matrix?
Answer : Yes, it would assuming none of the elements of the original matrix were imaginary......you said "complex" and generally that means a number that has both a real and an imaginary part. ....but if the original matrix had an imaginary number as one of its elements, then after you transposed it you would of course have to change the signs of all the imaginary elements even though they were not strictly "complex".. More from Yahoo Answers
Answer : Yes, it would assuming none of the elements of the original matrix were imaginary......you said "complex" and generally that means a number that has both a real and an imaginary part. ....but if the original matrix had an imaginary number as one of its elements, then after you transposed it you would of course have to change the signs of all the imaginary elements even though they were not strictly "complex".. More from Yahoo Answers
Question : It's a question on my math homework, and I figured out how to find the transpose of a matrix but I don't know under what circumstances would I need to do it.
Answer : Good question. I don't know how advanced you are in matrices, but at some point you'll learn how to set up and solve a set of simultaneous equations in matrix form. When the number of equations exceeds the number of unknowns, you'll learn how to get what's called the "least squares" solution, which involves the use of the transpose of your coefficient matrix. It will probably be a while before you get to this point, but there will be a point where you'll see the value of transposing a matrix... More from Yahoo Answers
Answer : Good question. I don't know how advanced you are in matrices, but at some point you'll learn how to set up and solve a set of simultaneous equations in matrix form. When the number of equations exceeds the number of unknowns, you'll learn how to get what's called the "least squares" solution, which involves the use of the transpose of your coefficient matrix. It will probably be a while before you get to this point, but there will be a point where you'll see the value of transposing a matrix... More from Yahoo Answers
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