Linear-transformation sentence example

linear-transformation
  • The present article is merely concerned with algebraical linear transformation.
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  • A theory of matrices has been constructed by Cayley in connexion particularly with the theory of linear transformation.
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  • The adjoint determinant will be seen subsequently to present itself in the theory of linear equations and in the theory of linear transformation.
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  • F(a ' a ' a, ...a) =r A F(ao, a1, a2,���an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.
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  • To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, I�1, A2, �2.
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  • The invariants in question are invariants qud linear transformation of the forms themselves as well as qud linear transformation of the variables.
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  • Taking the variables to be x, y and effecting the linear transformation x = X1X+1.11Y, y = X2X+It2Y, X 2 +Y2X Y Xl - X2 y = _ x X I + AI R X 122 so that - �l b it is seen that the two lines, on which lie (x, y), (X, Y), have a definite projective correspondence.
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  • The linear transformation replaces points on lines through the origin by corresponding points on projectively corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds projectively, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.
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  • To choose a basis with respect to which the matrix of a linear transformation has a particularly manageable form.
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  • F(a ' a ' a, ...a) =r A F(ao, a1, a2,���an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.
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  • To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, I�1, A2, �2.
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  • Taking the variables to be x, y and effecting the linear transformation x = X1X+1.11Y, y = X2X+It2Y, X 2 +Y2X Y Xl - X2 y = _ x X I + AI R X 122 so that - �l b it is seen that the two lines, on which lie (x, y), (X, Y), have a definite projective correspondence.
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  • Then there is a linear transformation A which takes x to y and u j to v j.
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