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Is the matrix the same after elementary transformation
Of course not! In addition to not changing the rank of the matrix, the properties of all other matrices have been changed!
However, the obtained matrix is equivalent to the original matrix
Given the line segment AB, take a point C on the extension line of Ba so that Ca = 3AB, then the ratio of the line segment CA to CB is
Four options:
A.3：4
B.2：3
C.3：5
D.1：2
A
Given the line segment AB, take a point C on the extension line of Ba so that Ca = 3AB, then the ratio of the line segment CA to the line segment CB is ()
A. 3：4B. 2：3C. 3：5D. 1：2
As shown in the figure above, ∵ CA = 3AB ∵ CB = Ca + AB = 4AB ∵ CA: CB = 3:4
Given the line segment AB, extend Ba to C so that Ca = 3AB. Point a is the equivalency of line segment CB
C⊙.A⊙.B⊙
CB=4AB
What is the equivalency of line CB at point a?
Ca / AB = 3 / 1, point a is the third quarter of line CB
It is known that as shown in the right figure, the line segment AB extends Ba to C so that Ca = 3AB. C_____________ A______ What fraction of B segment CA is CB?
CA=3AB
AB=CA/3
CA+AB=CB=4AB=4CA/3
CA/CB=3/4
So the segment CA is three fourths of the segment CB
Given the line AB, take a point C on the extension line of Ba so that Ca = 3AB, then CB=______ AB．
CA = 3AB, CB = Ca + AB = 4AB, so the answer is 4
What is the nature of matrix contract? Also, if the matrix is similar, is it a contract?
What is the nature of the matrix contract? Also, if the matrix is similar, then it must be a contract? Answer: the following is sorted out according to the net text, without strict proof analysis, for reference only. Proposition 1: real symmetric matrix A is similar to real diagonal matrix B; then a is similar to B. in short: two real symmetric matrices are similar, so it must be a contract
Which friend can explain the relationship between matrix equivalent and similar contract?
I think:
1. Similarity can lead to equivalence
2. Under the condition of symmetric matrix, similarity can deduce contract
Or who can give a better induction~
Equivalence means that two matrices have the same rank
Contract means that the positive definiteness of two matrices is the same, that is to say, the corresponding eigenvalue symbols of two matrices are the same
Similarity means that the eigenvalues of two matrices are the same
Similarity must be a contract, and contract must be equivalent
Why can't we deduce a contract when matrix A and B are equivalent
The contract requires a symmetric matrix, and equivalence (not similarity) is not necessarily a square matrix
Is an equivalent matrix a similar matrix? What's the difference between them?
Matrix equivalence: for matrix A (m * n), if there is an invertible matrix P and Q such that PAQ = B, then B is equivalent to A. in essence, a obtains B through a finite number of elementary transformations. Let a and B be matrices of order n. if there is a nonsingular matrix P of order n such that P ^ (- 1) * a * P = B holds, then matrix A is similar to B, denoted as a ~ B
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