# Scalars & Vectors

### Scalars & Vectors

As such, we’ll only be considering matrices with which you’re already familiar — no new ground. However, by the end of the section hopefully you’ll have started to appreciate the benefits of including matrices in your life as opposed to only vectors. Let’s start with this slide: This shows four vectors — the red ones represent a, b, c, and d. If you had previously only used column vectors, you may not have been able to tell a, b, c, and d apart. You may assume “a, b, c, and d are just numbers”. In contrast, the matrix looks like: It may look like a completely different ball game altogether. It could even be totally confusing. All you know is that it consists of four columns, where each is a new row and each row consists of four new numbers, and that there are four numbers. But what isn’t visually obvious is that the matrix representation allows you to work with the geometry of the vectors. A cool example of this that we’ve done in the past is a coordinate conversion where we could convert the coordinates of a point between all three vector representations (column, row, matrix). If we do that we get the point with coordinates (4, 23, 85): This is because when we look at the column vector representation of our x, y, and z coordinate we can immediately tell which is which: When we look at the matrix representation we can tell the same thing for the first two numbers because the numbers are repeated from column to column: That seems like a really useful property to have, but each coordinate is given to us alone. Now, let’s see what the matrix representation brings to the table: No longer are we stuck with numbers for each coordinate. Now we’ve got vectors and matrices working together to give us a unique representation of all points in space.

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You could even see this mathematically by looking at the matrix: As long as A, B, C, and D are matrices that satisfy the row and column operations of matrices, then A, B, C, and D will satisfy all other matrices as well. But not all matrices are an arbitrarily correct transform.Scalars & Vectors Getting Started All values in MaxLive are represented as floating-point numbers, except where stated otherwise. The default precision is double precision. It is also a good idea to use the values in Max as their default format. The value precision and format parameters for format lists specify the minimum and maximum precision of strings used to build the output formatter. Thus, if the output is already formatted the format values do not change the values in Max. If the format strings are for building the output formatter, then the source input data is expanded so they use a default precision. If the values being formatted are all expanded, the format strings will use the default precision. To change a data format of strings for an input value to a different number of decimal places, increase the precision of the data of the input; to change the data format of a Max string to a different number of decimal places, extract the string from the data input; if the data is floating point, change the number of decimal places using Scientific or Engineering notation, and round the value. Getting, setting, querying, and printing a value at its default floating point precision and formatting provides the most accuracy. This contrasts with setting values to a specific number of decimal places, parsing them as a fixed-point number, or to scientific notation when decimal places may not exactly correspond. To select a specific format in which to store or print a value, use the Value class.

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To select another format, use its constructor or method to pick the default formatting. Precision Parameters unit A numeric unit in scientific notation—for example, d, s, ms, or ns. The unit is stored in the data or string value. A default unit of ps is accepted. A unit specification of no unit is accepted; this is the same as specifying a unit value of ‘ps’. When the unit is ‘ps’, the value is stored as multiples of the last occurrence of the unit type, allowing for rounding issues. If the precision of the data or string output is low, the precision is approximated using the type of the amount with the unit value in type specification. step A official source step of the specified unit. For example, to print the output in the MSP seconds unit, the following is a valid specification: val = ‘MSP sec’. The unit type and value in the specification indicates the type of the data, and step is used to determine what integer number to output in the data type representation. The value and type are independent of any unit of the step. The precision of the data to be checked is adjusted by the value of the precision parameter, but this does not limit the precision of the format specifier, and therefore

Scalars & Vectors
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