Tell, please, what are the $\prec$ and $\succ$ operators for when you use it with matrices?

Zerrilloh6
2021-12-08
Answered

Tell, please, what are the $\prec$ and $\succ$ operators for when you use it with matrices?

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Pademagk71

Answered 2021-12-09
Author has **34** answers

Most commonly, the relation $A\succ B$ is used to indicate "A-B" is positive definite.

$A\succ 7.3$ means $A\succ 7.3I$ ; that is, "A is symmetric, and its eigenvalues are greater than 7.3."

Ben Owens

Answered 2021-12-10
Author has **27** answers

The name of this $\succ$ operator in the matrices is succeed and is $\prec$ precedes.

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Find a basis for the space of $2\times 2$ diagonal matrices.

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Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

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