$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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definition
concepts
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Two matrices $A$ and $B$ are row equivalent if we can get from $A$ to $B$ with a finite amount of row operations.
The elementary row operations are
  • multiply a row by a nonzero scalar
  • add the scalar multiple of a row to another
  • interchange rows
and each operation can be undone or inverted with another elementary row operation of some kind.

Concepts

Coming soon

Used In

Definitions: Proofs:
  • Every matrix is row equivalent to a row reduced matrix

Hypothesis

If two matrices are row equivalent, then:
  • They have the same nullspace
If a matrix is row equivalent to the identity matrix, then
  • It is invertible

Results

Two matrices are row equivalent if:
  • They have the same null space
A matrix is row equivalent to the identity matrix if:
  • It is invertible.
Two matrices $A$ and $B$ are row equivalent if we can get from $A$ to $B$ with a finite amount of row operations.
The elementary row operations are
  • multiply a row by a nonzero scalar
  • add the scalar multiple of a row to another
  • interchange rows
and each operation can be undone or inverted with another elementary row operation of some kind.

Concepts

Coming soon

Used In

Definitions: Proofs:
  • Every matrix is row equivalent to a row reduced matrix

Hypothesis

If two matrices are row equivalent, then:
  • They have the same nullspace
If a matrix is row equivalent to the identity matrix, then
  • It is invertible

Results

Two matrices are row equivalent if:
  • They have the same null space
A matrix is row equivalent to the identity matrix if:
  • It is invertible.
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
Two matrices $A$ and $B$ are row equivalent if we can get from $A$ to $B$ with a finite amount of row operations.
The elementary row operations are
  • multiply a row by a nonzero scalar
  • add the scalar multiple of a row to another
  • interchange rows
and each operation can be undone or inverted with another elementary row operation of some kind.

Concepts

Coming soon

Used In

Definitions: Proofs:
  • Every matrix is row equivalent to a row reduced matrix

Hypothesis

If two matrices are row equivalent, then:
  • They have the same nullspace
If a matrix is row equivalent to the identity matrix, then
  • It is invertible

Results

Two matrices are row equivalent if:
  • They have the same null space
A matrix is row equivalent to the identity matrix if:
  • It is invertible.
Two matrices $A$ and $B$ are row equivalent if we can get from $A$ to $B$ with a finite amount of row operations.
The elementary row operations are
  • multiply a row by a nonzero scalar
  • add the scalar multiple of a row to another
  • interchange rows
and each operation can be undone or inverted with another elementary row operation of some kind.

Concepts

Coming soon

Used In

Definitions: Proofs:
  • Every matrix is row equivalent to a row reduced matrix

Hypothesis

If two matrices are row equivalent, then:
  • They have the same nullspace
If a matrix is row equivalent to the identity matrix, then
  • It is invertible

Results

Two matrices are row equivalent if:
  • They have the same null space
A matrix is row equivalent to the identity matrix if:
  • It is invertible.
FullPage
definition
concepts
used in
hypothesis
results