TensorFlow Tensor Operations: Your Magic Toolbox 🧰

Imagine you have a giant box of LEGO blocks. Each block has a number on it. TensorFlow lets you play with millions of these blocks at once — stacking them, adding them together, or finding the biggest one. Let’s learn all the cool tricks!

🎯 The Big Picture

Tensors are like organized boxes of numbers. Think of:

• A single LEGO block = a number (scalar)
• A row of blocks = a list (1D tensor)
• A flat LEGO plate = a table (2D tensor)
• A 3D LEGO castle = a cube of numbers (3D tensor)

Today, we’ll learn 7 super powers to work with these LEGO towers!

1. 🔍 Tensor Indexing and Slicing

What Is It?

Picking out specific blocks from your LEGO tower.

The Story

Imagine you have a bookshelf with 5 shelves, and each shelf has 4 books. Sometimes you want:

• Just the 3rd book on the 2nd shelf
• All books on shelf 1
• The first 2 books from every shelf

That’s indexing (picking one thing) and slicing (picking a range)!

How It Works

import tensorflow as tf

# A bookshelf: 3 shelves, 4 books each
shelf = tf.constant([
    [10, 20, 30, 40],
    [50, 60, 70, 80],
    [90, 100, 110, 120]
])

# Get book at shelf 1, position 2
book = shelf[1, 2]  # Result: 70

# Get ALL books on shelf 0
row = shelf[0]  # [10, 20, 30, 40]

# Get first 2 books from shelf 2
slice_books = shelf[2, :2]  # [90, 100]

🎨 Visual

graph TD
    A["Full Shelf<br/>[3 x 4]"] --> B["shelf[1, 2]<br/>= 70"]
    A --> C["shelf[0]<br/>= [10,20,30,40]"]
    A --> D["shelf[2, :2]<br/>= [90, 100]"]

Key Rules

2. 🔄 Tensor Shape Manipulation

What Is It?

Reshaping your LEGO tower without losing any blocks.

The Story

You have 12 LEGO blocks in a line. You can arrange them as:

• 1 row of 12
• 2 rows of 6
• 3 rows of 4
• 4 rows of 3
• 6 rows of 2
• A 3D cube (2 × 2 × 3)

The blocks stay the same — only the shape changes!

How It Works

# Start with 12 numbers in a line
line = tf.constant([1,2,3,4,5,6,7,8,9,10,11,12])

# Reshape to 3 rows, 4 columns
table = tf.reshape(line, [3, 4])
# [[1,2,3,4], [5,6,7,8], [9,10,11,12]]

# Reshape to 2x2x3 cube
cube = tf.reshape(line, [2, 2, 3])

# Flatten back to a line
flat = tf.reshape(cube, [-1])  # -1 means "figure it out"

🎨 Visual

graph TD
    A["[1,2,3,4,5,6,7,8,9,10,11,12]<br/>Shape: #40;12,#41;"]
    A -->|"reshape [3,4]"| B["[[1,2,3,4],<br/>[5,6,7,8],<br/>[9,10,11,12]]<br/>Shape: #40;3,4#41;"]
    A -->|"reshape [2,2,3]"| C["3D Cube<br/>Shape: #40;2,2,3#41;"]
    B -->|"reshape [-1]"| D["Back to line<br/>Shape: #40;12,#41;"]

Useful Shape Functions

3. 🎭 Type Casting

What Is It?

Converting blocks from one material to another (plastic to wood, wood to metal).

The Story

Numbers come in different types:

• Integers (whole numbers): 1, 2, 3, -5
• Floats (decimals): 1.5, 3.14, -2.7

Sometimes you need to convert between them — like exchanging coins for bills!

How It Works

# Integer tensor
ages = tf.constant([25, 30, 35])
print(ages.dtype)  # int32

# Convert to float
ages_float = tf.cast(ages, tf.float32)
# Result: [25.0, 30.0, 35.0]

# Float to integer (cuts off decimals!)
prices = tf.constant([19.99, 5.50, 12.75])
prices_int = tf.cast(prices, tf.int32)
# Result: [19, 5, 12] ← decimals lost!

# Check type before operations
a = tf.constant([1, 2, 3])        # int32
b = tf.constant([1.0, 2.0, 3.0])  # float32
# a + b would ERROR! Must cast first.
result = tf.cast(a, tf.float32) + b

Common Types

4. ➕ Tensor Arithmetic

What Is It?

Math with LEGO blocks — adding, subtracting, multiplying, dividing whole towers at once!

The Story

Imagine you have two identical LEGO plates with numbers:

• Plate A: [10, 20, 30]
• Plate B: [1, 2, 3]

Adding them means: add block 1 from A to block 1 from B, and so on. Result: [11, 22, 33]

It’s like having robot helpers that do the same math on every block simultaneously!

How It Works

a = tf.constant([10, 20, 30])
b = tf.constant([1, 2, 3])

# Addition
add = a + b  # [11, 22, 33]

# Subtraction
sub = a - b  # [9, 18, 27]

# Multiplication (element-wise)
mul = a * b  # [10, 40, 90]

# Division
div = a / b  # [10.0, 10.0, 10.0]

# Power
power = a ** 2  # [100, 400, 900]

# With a single number (scalar)
double = a * 2  # [20, 40, 60]

🎨 Visual

graph LR
    A["[10, 20, 30]"]
    B["[1, 2, 3]"]
    A -->|"+"| C["[11, 22, 33]"]
    A -->|"*"| D["[10, 40, 90]"]

Arithmetic Operations Table

5. 📊 Tensor Reduction Operations

What Is It?

Summarizing your LEGO tower into fewer numbers — like finding the total, average, or biggest block.

The Story

You have test scores for 3 students across 4 subjects:

         Math  Science  English  Art
Alice     90      85       88    92
Bob       78      82       75    80
Carol     95      90       92    88

Reductions help you answer:

• What’s each student’s average? (reduce across subjects)
• What’s the highest score in each subject? (reduce across students)
• What’s the total of all scores? (reduce everything)

How It Works

scores = tf.constant([
    [90, 85, 88, 92],
    [78, 82, 75, 80],
    [95, 90, 92, 88]
])

# Sum of ALL scores
total = tf.reduce_sum(scores)  # 1035

# Average per student (axis=1 = across columns)
avg_per_student = tf.reduce_mean(scores, axis=1)
# [88.75, 78.75, 91.25]

# Max in each subject (axis=0 = across rows)
max_per_subject = tf.reduce_max(scores, axis=0)
# [95, 90, 92, 92]

# Find minimum
min_score = tf.reduce_min(scores)  # 75

🎨 Visual

graph TD
    A["3x4 Score Table"]
    A -->|"reduce_sum#40;#41;"| B["1035<br/>#40;total#41;"]
    A -->|"reduce_mean#40;axis=1#41;"| C["[88.75, 78.75, 91.25]<br/>#40;student averages#41;"]
    A -->|"reduce_max#40;axis=0#41;"| D["[95, 90, 92, 92]<br/>#40;subject max#41;"]

Reduction Functions

6. 🔢 Matrix Multiplication

What Is It?

A special way to combine two tables that’s the heart of neural networks!

The Story

Matrix multiplication is NOT just multiplying matching blocks. It’s more like a voting system:

Imagine:

• Matrix A = 3 students’ skills in different areas
• Matrix B = how much each skill matters for different jobs

Matrix multiplication tells you: how well each student fits each job!

The Rule

For A (shape m×n) × B (shape n×p) → Result (shape m×p)

Key: The inner numbers must match! (n = n)

How It Works

# 2 students, 3 skills each
students = tf.constant([
    [1, 2, 3],  # Student A
    [4, 5, 6]   # Student B
])  # Shape: (2, 3)

# 3 skills, 2 jobs
job_weights = tf.constant([
    [1, 0],   # Skill 1
    [0, 1],   # Skill 2
    [1, 1]    # Skill 3
])  # Shape: (3, 2)

# Matrix multiplication
fit_scores = tf.matmul(students, job_weights)
# Result shape: (2, 2)
# [[4, 5],   ← Student A fits
#  [10, 11]] ← Student B fits

Calculation Breakdown

Student A, Job 1: (1×1) + (2×0) + (3×1) = 4
Student A, Job 2: (1×0) + (2×1) + (3×1) = 5
Student B, Job 1: (4×1) + (5×0) + (6×1) = 10
Student B, Job 2: (4×0) + (5×1) + (6×1) = 11

🎨 Visual

graph LR
    A["#40;2, 3#41;"] -->|"× #40;3, 2#41;"| B["#40;2, 2#41;"]
    C["Inner dims must match<br/>3 = 3 ✓"]

Ways to Multiply

7. 📡 Tensor Broadcasting

What Is It?

TensorFlow’s magic to make mismatched shapes work together!

The Story

You want to add:

• A single number (1 block)
• To a whole row (5 blocks)

Normally, shapes must match. But broadcasting stretches the smaller tensor to fit!

It’s like having a magic copier that duplicates your single block 5 times automatically.

How It Works

# Adding a scalar to a vector
vector = tf.constant([1, 2, 3, 4, 5])
scalar = tf.constant(10)

result = vector + scalar
# [11, 12, 13, 14, 15]
# The 10 was "broadcast" to [10, 10, 10, 10, 10]

# Adding a column to each column of a matrix
matrix = tf.constant([
    [1, 2, 3],
    [4, 5, 6]
])  # Shape: (2, 3)

column = tf.constant([[10], [20]])  # Shape: (2, 1)

result = matrix + column
# [[11, 12, 13],
#  [24, 25, 26]]

Broadcasting Rules

1. Compare shapes from right to left
2. Dimensions must be equal OR one of them is 1
3. Size-1 dimensions get stretched

🎨 Visual

graph TD
    A["#40;2, 3#41; + #40;2, 1#41;"]
    A --> B["#40;2, 1#41; stretches to #40;2, 3#41;"]
    B --> C["Result: #40;2, 3#41;"]

Broadcasting Examples

🎁 Summary: Your 7 Super Powers

🚀 You Did It!

You now have 7 powerful tools in your TensorFlow toolbox. These operations are the building blocks for:

• Neural networks
• Image processing
• Natural language processing
• And so much more!

Remember: Every AI model is just these simple operations, stacked together cleverly. You’ve got this! 💪