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INDEX

center of line of second order, 63 nonsingular, 10
line rank, 14
general in space, 71 properties, 15
general on plane, 44 theorem, 14, 15
normal, 48 singular, 10
parametric, 74 square, 10
passing through two points, 73 transposition, 6
that crosses two points, 47 unit, 10
that goes through point and is parallel to zero, 11
direction, 46 matrix operations
vector, 74 properties, 11
with angle coefficient, 46 minor, 7
plane mixed product, 37
general, 66 geometric essence, 38
in segments, 68 in coordinates, 38
normal, 69 properties, 37
passing through three given points, 67 multiplication of
straight line, 42 matrix into digit, 11
equivalent matrices, 14 matrix into matrix, 11
expansion of determinant by elements of some vector by digit, 23, 26
row or column, 8
normal multiplier, 49
hyperbola, 55
directrix, 59 one-sheet hyperboloid, 79
eccentricity, 58 properties, 79
focus, 55 origin of system, 20
properties, 56
parabola, 60
hyperbolic paraboloid, 82
focus, 60
properties, 82
parameter, 60
Kramer’s formulas, 9 properties, 61
parallel shift of axes, 41
line parametric equations, 43
normal equation perpendicularity of lines, 50
properties, 48 plane
normal to given line, 48 general equation
line and plane in space, 77 properties, 66
line of second order, 51 pole, 40
projection of
matrix, 5, 10 product of vector and digit, 25
-column, 10 subtraction of vectors, 25
-row, 10 sum of two vectors, 25
basic transformations, 14 vector onto axis, 24
diagonal, 10 vector onto direction of vector, 33
diagonal element, 10 properties of linear operations, 23
element, 10 properties of three vectors in space, 29
elementary transformations, 14
entry, 10 radius-vector of point, 26
inverse, 12 rectangular coordinates of point, 20
theorem, 12 rectangular coordinates of vector, 30
minor, 14 reduce to canonical view, 62

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