renolovexoxo said:Homework Statement
Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.
Homework Equations
They define u x v as
u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2])
For any vectors u,v,w in R3, w.(uxv)=D(w,u,v)
Ax.y=x.A^Ty
The Attempt at a Solution
I'm not really sure how to find a standard matrix for this, so I haven't made much progress.
A Standard Matrix of Linear Transformation is a matrix representation of a linear transformation. It is a square matrix that maps input vectors to output vectors in a linear transformation. The columns of the matrix represent the images of the standard basis vectors under the transformation.
A Standard Matrix of Linear Transformation is determined by applying the transformation to the standard basis vectors and then arranging the resulting vectors as columns in a matrix. The order of the vectors in the matrix corresponds to the order of the basis vectors used for the transformation.
A Standard Matrix of Linear Transformation is used to easily and efficiently perform calculations involving linear transformations. It allows for the transformation of vectors to be represented in a compact way, making it easier to manipulate and analyze.
No, a Standard Matrix of Linear Transformation can only be used for linear transformations. Linear transformations are those that preserve vector addition and scalar multiplication, and can be represented by a matrix.
A Standard Matrix of Linear Transformation is a special type of matrix that is used to represent linear transformations. It is related to other types of matrices, such as identity matrices and zero matrices, which can be used to perform specific types of transformations. However, the Standard Matrix of Linear Transformation is unique in that it can represent any type of linear transformation.