Explain briefly,if V and W are of dimensions m and n respectively over F,then Hom(V,W) is of dimension mn over F.

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Posted on Jan 02, 2017

Just add the three vectors together. The first vector is 0.0i + 4.0j . The second vector is about 1.4i - 1.4j . The third is about -0.7i - 0.7j .

Adding the three vectors together gives about 0.7i + 1.9j .The exact answer is sqrt(0.5)i + (4.0-3sqrt(0.5))j .

Adding the three vectors together gives about 0.7i + 1.9j .The exact answer is sqrt(0.5)i + (4.0-3sqrt(0.5))j .

Mar 15, 2013 | Camping, Backpacking & Hiking

Because of Einstein, we often call time the fourth dimension. Special relativity shows that time behaves surprisingly like the three spatial dimensions. The Lorenz equations show this. Length contracts as speed increases. Time expands as speed increases.

Scientists have been graphing time, as if it were a length, for hundreds of years. To the left is a typical graph, showing two things in motion at the same speed, one to the left and one to the right. Time never behaves exactly like a spatial dimension. You cannot go backward in time. And you normally cannot go forward at different rates. But, there are surprising parallels. For some purposes, it is handy to call time a fourth dimension. For other purposes, it is not.

Pretend, for a moment, that there are more than three spatial dimensions. What is a four or five-dimensional cube like? It is hard to visualize. But, we can make a few deductions about such an object. What if a 5-dimensional cube is 2 centimeters on a side, what is its 5-dimensional volume? Well, we can easily generalize from the first three dimensions. A 2x2 square is 4 (2x2) square centimeters in area. A 2x2x2 cube is 8 (2x2x2) cubic centimeters in volume. A 2x2x2x2x2 5-dimensional cube is 32 centimeters-to-the-5th-power in 5-dimensional volume. None of that can be visualized. But, it makes sense. What is the distance between two points in 5-space? You can easily deduce a 5-dimensional Pythagorean Theorem.

A science fiction story says that time is the fourth dimension, and space is the fifth. Space is the first three dimensions

Scientists have been graphing time, as if it were a length, for hundreds of years. To the left is a typical graph, showing two things in motion at the same speed, one to the left and one to the right. Time never behaves exactly like a spatial dimension. You cannot go backward in time. And you normally cannot go forward at different rates. But, there are surprising parallels. For some purposes, it is handy to call time a fourth dimension. For other purposes, it is not.

Pretend, for a moment, that there are more than three spatial dimensions. What is a four or five-dimensional cube like? It is hard to visualize. But, we can make a few deductions about such an object. What if a 5-dimensional cube is 2 centimeters on a side, what is its 5-dimensional volume? Well, we can easily generalize from the first three dimensions. A 2x2 square is 4 (2x2) square centimeters in area. A 2x2x2 cube is 8 (2x2x2) cubic centimeters in volume. A 2x2x2x2x2 5-dimensional cube is 32 centimeters-to-the-5th-power in 5-dimensional volume. None of that can be visualized. But, it makes sense. What is the distance between two points in 5-space? You can easily deduce a 5-dimensional Pythagorean Theorem.

A science fiction story says that time is the fourth dimension, and space is the fifth. Space is the first three dimensions

Sep 17, 2011 | Computers & Internet

From the manual:

- You entered an argument with an inappropriate dimension.
- You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.
- You attempted to invert a matrix that is not a square matrix.

Nov 03, 2010 | Texas Instruments TI-86 Calculator

From the manual:

- You entered an argument with an inappropriate dimension.
- You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.
- You attempted to invert a matrix that is not a square matrix.

Nov 02, 2010 | Texas Instruments TI-86 Calculator

From the manual:

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were plotting or attempting to plot when you got this error.

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were plotting or attempting to plot when you got this error.

Sep 17, 2010 | Texas Instruments TI-86 Calculator

From the manual:

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were graphing or attempting to graph when you got this error.

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were graphing or attempting to graph when you got this error.

Sep 09, 2010 | Texas Instruments TI-86 Calculator

From the manual:

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were doing or attempting to do when you got this error.

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were doing or attempting to do when you got this error.

Aug 28, 2010 | Texas Instruments TI-86 Calculator

From the manual:

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were plotting or attempting to plot when you got this error.

You entered an argument with an inappropriate dimension.

You entered a matrix or vector dimension less than 1 or greater than 255 or a non-integer.

You attempted to invert a matrix that is not a square matrix.

If you can't figure it out from here, please reply to this post telling us what you were plotting or attempting to plot when you got this error.

Jun 06, 2010 | Texas Instruments TI-86 Calculator

Three possibilities:

1) You entered an argument with an inappropriate dimension.

2) You entered a matrix or vector dimension < 1 or > 255 or a noninteger.

3) You attempted to invert a matrix that is not a square matrix.

If you need further help, please specify the exact problem you're trying to solve.

1) You entered an argument with an inappropriate dimension.

2) You entered a matrix or vector dimension < 1 or > 255 or a noninteger.

3) You attempted to invert a matrix that is not a square matrix.

If you need further help, please specify the exact problem you're trying to solve.

Feb 10, 2010 | Texas Instruments TI-86 Calculator

FINISHED ROUGH OPENING DIMENSIONS: WIDTH = 47 1/2" HEIGHT = 83 3/4"

DIMENSION OF 532: H=84" W=48" D=24" MINIMUM HEIGHT=82 7/8" DOOR SWING=29 1/4"

DIMENSION OF 532: H=84" W=48" D=24" MINIMUM HEIGHT=82 7/8" DOOR SWING=29 1/4"

Mar 24, 2009 | Sub-Zero 690 Side by Side Refrigerator

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