Linear algebra: If the matrices a and b are equal, then the row vector group of a is equivalent to the row vector group of b Why? Linear algebra: If matrices a and b are equal, then the row vector group of a is equivalent to the row vector group of b. Why?

If matrix A A is equivalent to the matrix B, then the row vector group of the matrix A is equivalent to the row vector group of the matrix B. The above proposition does not necessarily hold because the matrix A is equivalent to the matrix B, i.e. there is a reversible matrix P, Q, such that PAQ=B, so PA=BQ^(-1) and P^(-1) B=AQ can not explain the row vector group of the matrix A and the matrix...

What is vector group equivalence and what is the condition for vector group equivalence

Here we have, which is not easy to copy:
Conditions for Vector Group Equivalence:
A ={ a1,a2,a3,...,an} B ={ b1,b2,b3,...,bn}
R (A)= r (A|bi) and r (B)= r (B|ai)(i=1,2,..., n)

There's something here that's hard to copy:
Conditions for Vector Group Equivalence:
A ={ a1,a2,a3,...,an} B ={ b1,b2,b3,...,bn}
R (A)= r (A|bi) and r (B)= r (B|ai)(i=1,2,..., n)

Is conditions of vector group equivalence, are both correct? The conditions of vector group equivalence, are both correct?

In general, the equivalence of matrices is defined first. The equivalence of two matrices means that a matrix can be transformed into another matrix by elementary transformation (it can also be subdivided into row equivalence (elementary row transformation only) and column equivalence (elementary column transformation only)). Because the vector group can form a matrix, the matrix in turn has row vector group and column direction.

Let the vectors a and b be nonzero, and under what conditions a+b is collinear with a-b

Because a+b is collinear with a-b a+b=K (a-b), ab is collinear

Linear algebra: If the matrices a and b are equal, then the row vector group of a is equivalent to the row vector group of b Why? Linear algebra: If matrices a and b are equal, then the row vector group of a is equivalent to the row vector group of b. Why?