- Hands-On Mathematics for Deep Learning
- Jay Dawani
- 128字
- 2021-06-18 18:55:10
Matrix transpose
Let's take an 
matrix A. If the matrix's transpose is B, then the dimensions of B are 
, such that: 
. Here is the matrix A:
Then, the matrix B is as given:
.
Essentially, we can think of this as writing the columns of A as the rows of the transposed matrix, B.
We usually write the transpose of A as AT.
A symmetric matrix is a special kind of matrix. It is an n×n matrix that, when transposed, is exactly the same as before we transposed it.
The following are the properties of inverses and transposes:
If A is an invertible matrix, then so is AT, and so (A-1)T = (AT)-1 = A-T.