Mit super position file 1 new

• A MATCHBOX CAR GOIMG 10 M/S AT NORTH EAST
• A MATCHBOX CAR GOIMG 10 M/S AT SOUTH EAST

Color box
The color can be inferred from the position

• Which again-has 3 apperatures-an input
• And hard electrons come out this port and soft elecrtron come out
this port

And the workings inside the box do not matter

You can imagine-so little worker inside the
box deciding what is extracted

The box can be built with dwarfs, elves, silver
atoms, atoms with a lot of neutrons, etc

But what ever they are built with-they give the
same results the professor is gonna describe

So-a chief property of the hardness and color
boxes is the ‘results are repeatable”

If I send in an electron and it comes out a
color box –black-SWITCH NOW TO FILE 2

Then, I send it in another color box-and it
comes out black again

So-in a diagram-if I say an “IN”

And –I discover that it comes out the white
apparature

And –I take the ones that come out the white
apperature –and I send them into a color box

With 100% confidence-meaning 100% of the
time

The electron coming out the white port and
into the color box

Will come out the white apperature again

Where to come out the black apperature

So –this is a persistent property

You notice that it is white-and it is still white

Dealing with hardness-if I send a bunch of
electrons in a hardness box

And I am going to isolate the ones that come
out soft

You have these images in google

What Is A Tensor Lesson #1: Elementary vector
spaces

WOULD BRAGG –COME OVER TO RACE
OTHER KIDS

And –some were faster than others
• A MATCHBOX CAR GOIMG 10 M/S AT SOUTH EAST

SOME SPACE—SPEDS- A COLLECT OF SPEEDS-
A TENSOR

A VECTOR SPACE-THE BOX OF CARS

WE CAN ADD BVELOCITIES OF THE CARS

WE CAN MULTIPLY THE- AND AND THE
SPEEDS-THEY HAVE THE SAME UNITS

NOW-LET’S SAY ROB –PETER AND ERIC ARE
GONNA RACE THEIR CARS-”TRUE STORY”

AND I SAID WE CAN ADD 10 M/S TO 20 M/S
TO MAKE 30 M/S GIONG NORTH

YOU CAN MULTIPLY THEM-THIS IS CALLED
SCALAR MULTIPLICATIO

WHEN YOU DO THIS-IT BECOMES AN
ELEMENT OF THE VECTOR SPACE
• LET ME RUN THIS BY YOU

THE PROCESS IS CALLED SCALAR
MULTIPLICATION

THE OBJECTS THAT COME OUT OF THE REAL
NUMBERS ARE CALLED SCALARS

THE TENSOR-COULD BE A BOSX SHAPE-BUT
ALSO COULD BE SHAPED LIKE ABALL

• Linear Algebra Example Problems - Vector Space Basis Example #2
• https://www.youtube.com/watch?v=vejkdUigyIg

• How to Prove a Set is a Subspace of a Vector Space
• https://www.youtube.com/watch?v=Eawc_ZuQI_8

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