Download An elementary exposition of Grassmann's Ausdehnungslehre, or by Joseph V. Collins PDF

By Joseph V. Collins

Excerpt from An easy Exposition of Grassmann's Ausdehnungslehre, or idea of Extension

The sum qf any variety of vectors is located by way of becoming a member of the start aspect of the second one vector to the tip aspect of the 1st, the start element of the 3rd to the top element of the second one. etc; the vector from the start aspect of the 1st vector to the tip aspect of the final is the sum required.

The sum and distinction of 2 vectors are the diagonals of the parallelogram whose adjoining facets are the given vectors.

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Additional resources for An elementary exposition of Grassmann's Ausdehnungslehre, or Theory of extension

Sample text

It also is used to indicate a positive number. ✓ – means subtract or minus or decreased by or less than; the result is the difference. It’s also used to indicate a negative number. ✓ × means multiply or times. The values being multiplied together are the multipliers or factors; the result is the product. Some other symbols meaning multiply can be grouping symbols: ( ), [ ], { }, ·, *. In algebra, the × symbol is used infrequently because it can be confused with the variable x. The dot is popular because it’s easy to write.

Consider the stock market (something that gets considered a lot these days). The news reporter declares that the Dow Jones went down 20 points twice in a row. You multiply two times –20 to get –40. So a positive times a negative is a negative. How about dividing? You and three friends decide to buy another friend lunch. 64. How much does each person chip in? 91 is what each of you contributes. When multiplying and dividing two signed numbers, if the two signs are the same, then the result is positive; when the two signs are different, then the result is negative.

It’s also used to indicate a negative number. ✓ × means multiply or times. The values being multiplied together are the multipliers or factors; the result is the product. Some other symbols meaning multiply can be grouping symbols: ( ), [ ], { }, ·, *. In algebra, the × symbol is used infrequently because it can be confused with the variable x. The dot is popular because it’s easy to write. The grouping symbols are used when you need to contain many terms or a messy expression. By themselves, the grouping symbols don’t mean to multiply, but if you put a value in front of a grouping symbol, it means to multiply.

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