Bright Zoom Maths

  Linear Algebra Symbols Symbol Symbol Name Meaning / definition Example · dot scalar product a  ·  b × cross vector product a  ×  b A ⊗ B tensor product tensor product of A and B A  ⊗  B inner product [ ] brackets matrix of numbers ( ) parentheses matrix of numbers |  A  | determinant determinant of matrix A det( A ) determinant determinant of matrix A ||  x  || double vertical bars norm A T transpose matrix transpose ( A T ) ij  = ( A ) ji A † Hermitian matrix matrix conjugate transpose ( A † ) ij  = ( A ) ji A * Hermitian matrix matrix conjugate transpose ( A * ) ij  = ( A ) ji A  -1 inverse matrix A A -1  =  I rank( A ) matrix rank rank of matrix A rank( A ) = 3 dim( U ) dimension dimension of matrix A rank( U ) = 3

  Algebra symbols Symbol Symbol Name Meaning / definition Example x x variable unknown value to find when 2 x  = 4, then  x  = 2 ≡ equivalence identical to ≜ equal by definition equal by definition := equal by definition equal by definition ~ approximately equal weak approximation 11 ~ 10 ≈ approximately equal approximation sin (0.01) ≈ 0.01 ∝ proportional to proportional to y  ∝  x  when  y  =  kx, k  constant ∞ lemniscate infinity symbol ≪ much less than much less than 1 ≪ 1000000 ≫ much greater than much greater than 1000000 ≫ 1 ( ) parentheses calculate expression inside first 2 * (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 { } braces set ⌊ x ⌋ floor brackets rounds number to lower integer ⌊4.3⌋ = 4 ⌈ x ⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉ = 5 x ! exclamation mark factorial 4! = 1*2*3*4 = 24 |  x  | single vertical bar absolute value | -5 | = 5 f  ( x ) function ...

  Geometry symbols Symbol Symbol Name Meaning / definition Example ∠ angle formed by two rays ∠ABC = 30° measured angle ABC = 30° spherical angle AOB = 30° ∟ right angle = 90° α = 90° ° degree 1 turn = 360° α = 60° deg degree 1 turn = 360deg α = 60deg ′ prime arcminute, 1° = 60′ α = 60°59′ ″ double prime arcsecond, 1′ = 60″ α = 60°59′59″ line infinite line AB line segment line from point A to point B ray line that start from point A arc arc from point A to point B  = 60° ⊥ perpendicular perpendicular lines (90° angle) AC ⊥ BC | | parallel parallel lines AB | | CD ≅ congruent to equivalence of geometric shapes and size ∆ABC≅ ∆XYZ ~ similarity same shapes, not same size ∆ABC~ ∆XYZ Δ triangle triangle shape ΔABC≅ ΔBCD | x - y | distance distance between points x and y |  x - y  | = 5 π pi constant π  = 3.141592654... is the ratio between the circumference and diameter of a circle c  =  π · d  = 2· π · r rad radians radians angle unit 360° = 2π rad c ...

  Basic math symbols Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 5 is equal to 2+3 ≠ not equal sign inequality 5 ≠ 4 5 is not equal to 4 ≈ approximately equal approximation sin (0.01) ≈ 0.01, x  ≈  y  means  x  is approximately equal to  y > strict inequality greater than 5 > 4 5 is greater than 4 < strict inequality less than 4 < 5 4 is less than 5 ≥ inequality greater than or equal to 5 ≥ 4, x  ≥  y  means  x  is greater than or equal to  y ≤ inequality less than or equal to 4 ≤ 5, x ≤ y  means  x  is less than or equal to  y ( ) parentheses calculate expression inside first 2 × (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)×(1+5)] = 18 + plus sign addition 1 + 1 = 2 − minus sign subtraction 2 − 1 = 1 ± plus - minus both plus and minus operations 3 ± 5 = 8 and -2 ± minus - plus both minus and plus operations 3 ± 5 = -2 and 8 * asterisk m...

Logical Reasoning skills  Logical Reasoning -Analogy  1. Complete analogous pair: Automobile : Petrol :: ? A. fire : fuel B. plane : propeller C. diesel : gas D. man : food Answer: D. man : food Explanation: An automobile needs petrol to function. Similarly, man needs food in order to function. 2. Complete analogous pair: Calf : cow :: Puppy : ? A. cub B. kitten C. dog D. snake Answer: C. dog Explanation: A calf's parent is cow and puppy's parent is dog. 3. Complete analogous pair: Tungsten : Filament :: Tree : ? A. graphite B. paper C. wool D. fabric Answer: B. paper Explanation: The first term is used in the production of the second. 4.Complete analogous pair: Letter : Word :: A. homework : school B. club : people C. product : factory D. page : book Answer: D. page : book Explanation: A group of letters form a word. Similarly, a group of pages combined together form a book. 5. Complete analogous pair. Brick : Clay :: Ruby : ? A. graphite B. corundum C. diamond D. pearl Answe...

 Logical Reasoning skills  Logical Reasoning -Solved Problems  1. Arrange the given words in a meaningful sequence. 1. Sentence, 2. Chapter, 3. Word, 4. Paragraph, 5. Book A. 2, 3, 1, 5, 4. B. 3, 2, 5, 4, 1. C. 5, 2, 4, 1, 3. D. 5, 3, 2, 4, 1. Answer: C. 5, 2, 4, 1, 3. Explanation: The correct order is: Book (5) - Chapter (2) - Paragraph (4) - Sentence (1) - Word (3). 2. In a row of 54 persons, A is 35th from the left side of the row and B is 22nd from the right side of the row. Find the no. of persons sitting between A and B? A. 1 B. 2 C. 3 D. 4 Answer: A. 1 Explanation:  Here Sum of positions of A & B from opposite ends = 35 + 22 = 57 > Total no. of persons ∴ No. of persons between A & B = (Position of A from left + Position of B from right) - Total no. of students - 2 No. of persons between A & B = (35+22) - 54 - 2  = 57 - 54 - 2 = 1. 3. Choose the pair in which the words are differently related. A. Cow : Fodder B. Crow : Carrion C. Poultry : F...

Logical Reasoning skills Logical Reasoning - Syllogism  1. Direction (1-7) : In each of the questions below three statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. 1. Statements: Some buildings are white. All whites are oranges. Some oranges are boxes. Conclusions: I. Some boxes are buildings. II. Some oranges are buildings. Answer: If only conclusion II follows. Explanation: Some buildings are white + All whites are oranges = I + A = I Some buildings are oranges - conversion - some oranges are buildings (I). Hence II follows. Some buildings are oranges + Some oranges are boxes = I + I = No Conclusions. Hence I does not follow.. 2. Statements: All desks are mirrors. All mirrors are chairs. Some chairs are...