Change of basis in Mathematica












2














I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question
























  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    2 days ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    2 days ago
















2














I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question
























  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    2 days ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    2 days ago














2












2








2







I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question















I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra




matrix mathematical-optimization linear-algebra






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 2 days ago

























asked 2 days ago









wznd

315




315












  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    2 days ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    2 days ago


















  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    2 days ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    2 days ago
















Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
– Henrik Schumacher
2 days ago




Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
– Henrik Schumacher
2 days ago




1




1




@HenrikSchumacher I'll edit the post then :)
– wznd
2 days ago




@HenrikSchumacher I'll edit the post then :)
– wznd
2 days ago










1 Answer
1






active

oldest

votes


















4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    2 days ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    2 days ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    2 days ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    2 days ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    2 days ago











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1 Answer
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active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

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active

oldest

votes









4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    2 days ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    2 days ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    2 days ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    2 days ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    2 days ago
















4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    2 days ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    2 days ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    2 days ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    2 days ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    2 days ago














4












4








4






This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True








share|improve this answer














share|improve this answer



share|improve this answer








edited 2 days ago

























answered 2 days ago









Henrik Schumacher

48.7k467139




48.7k467139












  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    2 days ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    2 days ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    2 days ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    2 days ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    2 days ago


















  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    2 days ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    2 days ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    2 days ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    2 days ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    2 days ago
















Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
– wznd
2 days ago




Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
– wznd
2 days ago












ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
– Henrik Schumacher
2 days ago




ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
– Henrik Schumacher
2 days ago












Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
– wznd
2 days ago




Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
– wznd
2 days ago












You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
– Henrik Schumacher
2 days ago




You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
– Henrik Schumacher
2 days ago












Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
– wznd
2 days ago




Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
– wznd
2 days ago


















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