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I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source which is far away.

The null space of this mapping is a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors which contain a component in the direction of the null space undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)

I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source which is far away.

The null space of this mapping is a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)

I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source.

The null space of this mapping is a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors which contain a component in the direction of the null space undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)

I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source which is far away.

The null space of this mapping is a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors which contain a component in the direction of the null space undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)

I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source.

The null space of this mapping is represented by a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors which contain a component in the direction of the null space undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)

I find the easiest way to visualise null space is to consider a matrix mapping which represents the mapping of a vector to its shadow on $y=0$ from a fixed light source.

The null space of this mapping is a vector pointing directly towards the light source, because the vector representing its shadow in $y=0$ will be $0$. Generally, we can see from this example that for some mappings there will exist vectors which will always be mapped to $0$.

We can also see how other vectors which contain a component in the direction of the null space undergo a non-invertible mapping. That is, from the shadow the best you could reconstruct the original vector would be up to an ambiguity in the direction of the null space.

(This is also good because you can do it on a table with a pen)